Prepare to take a ride on an emotional roller-coaster across the most challenging aspects of Russian language. Or should I rather correct the previous sentence, ‘descent into madness’. Some of my French and Luxembourgian friends married some of my Russian friends and are currently learning Russian in order to improve communication with their spouses and show devotion. Naïve martyrs, says me; little do they know that the system of conjugation and declension has so many illogicalities and exceptions that it is easier to say that there is absolutely no system to declension and conjugation. Let us begin, shall we?

1. In Russian, if one is narrating a story and wants to emphasise the suddenness of some action, one can substitute the 3rd person past indicative (singular or plural) with the 2nd person present imperative (singular only).
2. This works in reverse: one can use 2nd person past perfective to denote imperative!
3. In fact, when narrating, instead of 1st person past continuous, one can use just present (Russian does not have continuous tenses, neither it has present perfective.) However, incidentally, the present tense can also describe future events.

Original:

Шагаю я намедни по плацу, а у меня возьми и отойди пуговица на шинели.
Старшина тут же: «Быстро пришил пуговицу обратно!»
А я не могу, я встречаюсь с девушкой через час.

Verbatim translation:
I am marching the other day on the drill ground, and suddenly, you, button, ^imperativego and imperativefly off.
Sergeant: ‘You sewed this button back on!’
But I cannot waste time, I have a date in one hour!

Proper translation:
I was marching the other day on the drill ground, and suddenly, a button decided to fly off.
Sergeant: ‘Hey you, ^imperativesew this button back on!’
But I cannot waste time, I am having a date in one hour!

4. You know, in some languages, verbs have their own conjugation tables. Enormous tables for every single verb. Like conjugaison.com (from the creators of ‘j’aurais voulu que vous sussiez’ and ‘vous pûtes’). Some verbs do not necessarily make sense in certain forms (no one would say about themselves ‘I foal’, which means, to give birth to a colt—a baby horse). Russian has a verb for giving birth to a horse (жеребиться), but does not have its first-person form (жереблюсь? жеребюсь? ожеребляюсь?). Another example is the modification of ‘to head up’ for a wheat spike. If anyone here is a wheat spike, raise your awns. Some verbs do not have certain forms because they would just sound awful (бдеть, to keep vigil — бжу? бдю? бдею?; шерстить, to irritate someone’s skin with wool — шерщю? шерстю? шерщиваю?). So in Russian, those verb forms are substituted with ersatz expressions (сохраняю бдительность, я свитер, оттого я чешу и колюсь). Those are called insufficient verbs since they do not have certain forms. Do not be surprised if you cannot simply translate ‘I shall win’ using the future perfective form of the verb ‘to win’ because there is none (variants such as победю, побежу, побежду are all wrong)! You already lost when you started learning Russian.
5. Conversely, some verbs have two forms (such verbs are called superfluous). Of course, with slightly different meanings; otherwise, where would be fun in that? For example, the verb ‘cast’ would have the same infinitive but different indicative forms: ‘Zeus casts lightning bolts’ (Зевс мечет молнии) and ‘the athlete throws the hammer’ (спортсмен метает молот).
6. In Russian language, there is a special form of past tense, plus quam perfectum, or pluperfect (which, of course, is not listed in conjugation tables in textbooks dictionaries!), that is analogous to the English ‘used to / would’ or French ‘avait fait’. However, it is not past perfect in the traditional sense; it denotes a continuous action for which the speaker would like to evoke memories of the distant past. The simple past tense of the verb ходить (to walk) is ходил, but the pluperfect form is хаживал. In it is more or less analogous to the English ‘would’: ‘Back in the days of yore, my father would visit royal dinner parties and would try precious wine from Duke’s personal reserves. Oh, the yesteryears! Poor, poor father, where is he now! Those corks on the shelf from the bottles of wine he would savour are the last vestiges of the long-faded grandeur!’

Говорить — говаривал, петь — певал, сидеть — сиживал, есть — едал, ездать — езживал, гостить — гащивал, обедать — обедывал, драть — дирал, двигать — двигивал, махать — махивал, жить — живывал, гонять — ганивал, спать — сып́ал, кутить — кучивал, бегать — бегивал.

7. Also, one cannot just say, ‘there is a glass on the table’. Things on top of other things must either stand, lie, or sit, and there is no rule, logic or mnemonic to determine which verb to use.

There is a table. There is a glass on the table. It is standing (стакан стоит). There is a fork on the table. It is lying (вилка лежит). However, if we stick the fork into the table, it will be standing (or sticking out; будучи воткнутой в стол, вилка стоит вертикально). Maybe it is the horizontal / vertical orientation that matters? Let’s add a plate and a pan. They are horizontally oriented, but they are still standing (на столе стоят тарелка и сковородка). Now let’s place the plate inside the pan. Now it is lying in the pan (but it had been standing on the table; тарелка лежит в сковородке). The readiness of an object for use is not an indicator: the fork is lying. Not a cat jumps on the table. The cat can stand, sit or lie (кошка стоит, сидит или лежит). It is trivial to connect lying / standing with the cat’s orientation, but sitting? It is a new property. The cat’s bottom is instrumental in sitting (кошка сидит). Now a bird lands on the table. It is sitting as well (птица сидит). However, its legs are fully supporting its body, and in no way the bird is using its botty department. The bird, however, is never standing. Now we go berserk, kill the bird, and a taxidermist (probably Chuck Testa) stuffs it and makes a completely life-like bird—and now it is standing (чучело птицы стоит)! If you think that only animate object can sit, you are wrong again: a shoe sits on a foot, a dress sits on a person, a car sits in snow, a mosquito sits in amber (ботинок сидит на ноге, платье сидит на человеке, машина сидит в сугробе, комар сидит в янтаре). These objects are inanimate, do not have buttocks, but still, they are sitting! Now go figure out which objects sit, which stand, and which lie.

The Staffordshire department of the Royal Society of Putting Things on Top of Other Things must have accepted too many Russian members!

8. In Russian, plural is denoted in three possible ways: singular nominative, singular genitive, and... well, plural. It goes like this:

One cow, two ^ofcow, three ^ofcow, four ^ofcow, five cows, six cows... eleven cows, fourteen cows, and so it goes on until twenty cows. Then... you have twenty-one cow. Because it ends with one! Then, twenty-two... you guessed right... ^ofcow! Twenty-four ^ofcow, twenty-five cows, and so it goes on.

Everyone remembers Disney’s ‘101 dalmatian’, right?

9. A small but nasty one: while the words for 20, 30, 50, 60, 70, 80 and 90 are based on 2, 3, 5, 6, 7, 8 and 9 respectively (like two-ten, three-ten etc.), the word for 40 (сорок) does not have anything related to four. Instead, it is related to.... packed bundles of sable fur, why not! It is not the word forty that Russians used to describe the number of sable pelts in a bundle sufficient to make one coat; it is literally the word ‘cloth to wrap a bundle of sable pelts’ that Russians use for forty! The closest relative of this atrocity is the word сорочка (a shirt made of cloth), which is widely used as a synonym for рубашка.

Bulgarians did not have sables or martens, so in Bulgarian language (which is re-e-eally close to Russian), they use Russian numerals two-ten, three-ten, four-ten, five-ten etc. No animals harmed.

10. Worse than that, with compound numerals (like three thousand five hundred and seventy-four), one has to decline every word of the numeral. Sometimes, if a numeral is one word made of two parts (like ‘four-hundred’), you have to decline both. Or maybe not. Of course, if the numeral in question is fourteen, you do not decline the four, because screw fourteen! And two-ten, three-ten and four-ten as well. So it will look like this:

Я гордый владелец трёх тысяч пятисот семидесяти четырёх коров.
Я гордый владелец трёх тысяч трёхсот тридцати четырёх коров.
Я гордый владелец трёх тысяч семисот четырнадцати коров.

I am a proud owner ^ofthree ^ofthousand ^offive^ofhundred ^ofseven^often ^offour ^ofcows.
But! I am a proud owner ^ofthree ^ofthousand ^ofthree^ofhundred three^often ^ofthree ^ofcows.
But! I am a proud owner ^ofthree ^ofthousand ^ofseven^ofhundred four^ofteen ^ofcows.

Oh, and did I tell you that you have four more cases to remember for these numerals?

11. To make things worse, numerals ending with 1 or 2 can have genders in the nominative case. But only masculine or feminine. No neuter.

Два чайника, две чашки, два пальто.

12. Speaking of genders, verbs have genders in the past, but not in the present or future.

Металл кипел, сталь кипела, железо кипело, жидкости кипели.

13. Russian has different declension rules for animate and inanimate objects. However, a stiff is animate, while a corpse is not. Why? Well, only a human being can be a stiff, but corpses can also be of animal origins... so it makes dead animals less animate than dead humans? I hypothesise that this dates back to Russian folk tales in which stiffs came to life after being sprinkled with the Water of Life™ (they also featured the Water of Death™ that was used to join together the pieces of a fallen hero). However, the more logical reasoning is the following: the word мертвец (stiff) has a tinge of ‘freshness’ (just died), maybe clinical death, someone who had just died, but the word труп (corpse) denotes something that has been dead for a while. One does not exhumate stiffs; only corpses. In official language (forensic reports) one might use the collocation свежий труп (fresh corpse) to indicate that the body has not begun to rot yet.

Я вижу на земле мертвеца. (Accusative taking the form of genitive, as with animate objects.)
Я вижу на земле труп. (Accusative taking the form of nominative, as with inanimate objects.)

14. You thought it was over, huh? Cue fractional numerals! You all know that 8 metres should always be ‘eight metres’, no silly gobbledegook like ‘three ^ofcow’? Well... if it is 8.6 metres, it has to be spelt ‘eight and six tenths... ^ofmetre’, because it is the bloody tenths that govern the declension ‘of metre’! However, if one means ‘8½ metres’, it becomes ‘eight and a half metres’. Did I say that while ‘my pie’ is singular, ‘my half a pie’ is plural? Like ‘ton gâteau’ but ‘tes demi-gâteaux’!
15. Speaking of numerals. Most languages have cardinal numerals and ordinal numerals. However, Russian also has collective animate masculine numerals that sometimes describe groups of men, occupations (but possibly females), and uncountable singular nouns! One cannot say ‘two ^ofman’. One must say ‘two-group men’. Then, ‘three-group men’, up to ‘nine-group men’, although one can use the simple cardinal plural starting from 5. And one must not use collective numerals for groups larger than 10.
16. And some countable nouns have absolutely mental plural forms: дно — донья (bottom; almost like doña), брелок — брелоки (keychain, but чулок — чулки, stocking), шило — шилья (awl), профессор — профессора (professor). It gets better with genitive: кочерга — кочерёг (hot poker), кровля — кровель (roofing), усадьба — усадеб (manor), вафля — вафель (waffle), цапля — цапель (heron), кегля — кегель (bowling pin), but кегль — кеглей (typographic unit, from German Kegel).
17. If you thought it does not get worse, brace yourselves. Look at the word ‘human’. Look at it closely? Do you think it has two forms of plural, cardinal and collective? Well, here you are wrong again: three plural forms! It has collective plural (nobody matters), tally plural (each one matters), and archaic plural (for greater grandiloquence). It is like distinguishing between ‘many people’, ‘a number of individuals’ and ‘humanity’. (One could parry that kind of attack on sanity with an over-the-top number of collective nouns in the post-Norman tongue...)

We are approaching the culmination, or, as Kaikosru Sorabji would put it, ‘the crux’. Combining together muddy numerals and incoherent declension, one gets a new frankenrule: If the numeral ends with 1, 2, 3 or 4, one uses singular declension rules to denote multiplicity. However, in cases other than nominative, one uses plural for those one ending with 2, 3 or 4. If one thinks of those objects as of a large group performing an action, instead of the plural form of the verb, one can use the neuter singular! However, if the numeral ends with 1, one must use the singular form of the verb of the appropriate gender!

I did not make this up. This is true. Denoting accusative with ^den, as in German, we get the example to illustrate it:

Сто один далматинец переходил дорогу. Грузовик сбил сто одного далматинца.
Сто два далматинца переходило / переходили дорогу. Грузовик сбил сто двух далматинцев.
Сто пять далматинцев переходило / переходили дорогу. Грузовик сбил сто пять / пятерых далматинцев.

One hundred and one dalmatian was crossing the highway. The lorry ran over hundred and ^denone ^dendalmatian.
One hundred and two ^ofdalmatian was/were crossing the highway. The lorry ran over ^denhundred and ^dentwo ^dendalmatians.
One hundred and five dalmatians was/were crossing the highway. The lorry ran over ^denhundred and ^denfive / ^denfive-group ^dendalmatians.
(Here, one cannot say ‘сто двоих’, hundred and two-group, because it would mean, ‘hundred and both’!)

I have no words. The only thing I have is an back-of-the-envelope estimate: if kids start learning Russian at the age of 0 and by the age of 18, having graduated from high school, are aware of all these pitfalls, then it would take 18 years of intense learning (like at school, multiple hours per day of reading textbooks in Russian, watching TV, communicating with native speakers etc.) to master Russian. If you are a non-Russian reading this, the only way to comprehend Russian grammar is marrying a Russian and learning the language with your kid. By the time they reach the age of majority, you will be able to speak as fluently as they do.