Gort gave us:
This site should explain it nicely.
The Bayonet Strength site is a great resource for 1-to-1 unit scale wargamers.
But just looking at the Soviet formation TO&Es often does not lead to a better understanding, as the Soviets were pretty quick to change and adapt as their experience grew and circumstances changed during the war. You'd have to have an encyclopedic memory to keep it all in your head.
For the sake of understanding, it is better to keep a few basics in mind, and then just to accept that how those basics were applied changed over time.
A basic medium or light tank platoon was 3 tanks.
A basic medium or light tank company was 3 platoons plus a company command tank. 10 total. But ... sometimes only 2 platoons (when tanks were critically short in the winter of 41/42 through mid 42).
A basic medium or light tank battalion was 2 companies, plus a command tank. 21 total. (Thunder has it right.) The preference was actually for 3 companies per battalion, but after the openning phases of Barbarossa tanks were in such short supply, and commanders capable of handling larger formations were in such short supply, that smaller formations were the order of the day, and so for most of the war the battalion was 21 tanks. By late 1944 some 31 tank battalions started to re-appear.
A basic heavy tank platoon was 2 tanks.
A basic heavy tank company was 2 platoons plus company command tank early war, going to 3 platoons plus company command tank late war. 5 total, goes to 7 total.
Those are the basics. That is about as much as my poor mind can keep hold of reliably. Everything above that level is case-specific to points in time and locations on the front.
Larger formations changed a lot during the war. Pure medium tank regiments of 2 battalions plus a command tank (and support units) were the basic armored formation from mid-war on. But up to that point regiments occured in dozens of forms, and even battalions were often of mixed composition. Brigades were sometimes formed as well, which were at about the same level as regiments, but were intended for more independant roles, and so often had different supporting units.
Heavy tanks were assembled into any number of larger formations. Sometimes battalions, more often directly into regiments of 4 companies, with no battalion level in-between.
Heavy tanks were present in company strength in mixed battalions early war. Later they were usually combined into independant regiments of 3 or 4 companies with a command tank, with no battalion level command in-between.
And any unit in reality may have been short of these strengths, or of mixed composition, quite aside from what the authorized strength was. The Soviets loved organizing stuff centrally into theoretically uniform formations, but at the pointy end of the stick they used whatever they had.