As I could understand your question, you're more interested in passenger trains.
On main lines trains could be divided into following groups:
suburban which follow on distance in 50-200 km - usually EMU's consisting of 8-12 wagons (excepting small branches);
interurban trains can also be EMU's (but whith separate seats in II and I class wagons). Their trip length could reach 6-8 hours (about 500 km). But sometimes a loco with some passenger wagons with places for sitting could be used too. These trains are usually running in the daytime;
There are also 'distant' (that's difficult sometimes to find the correct english word) passenger trains (короче, ПДС :-). They look almost similar one to other, but are subdivided into categories depending on length and speed of the trip.
These trains consist of one, seldom two passenger locos and up to 17-20 wagons, the number of wagons depends on number of passengers; in winter, when the number of passengers decreases, trains of the same type and route could be coupled in one train of the normal length.
They are usually divided into categories:
'fast' (скорые) - they cover the long distance and have the smallest number of intermediate stops (up to every 200-400 km only to change the locomotive, mainly in large cities; it depends on length of the whole trip);
'distant' (дальние) - (subdivided into summer and all season) which could cover the same distance, but are a bit slower and make more intermediate stops.
The smallest length of the trip in these trains is the same as in the interurban and takes one night. The maximum length is unlimited
and could reach about a week.
There are also special trains, consisting of mail and luggage wagons only; they are pulled by passenger locos too, but have long stops, which are needed to load/unload them.
The typical consist of such train includes a restaurant car in the middle of the train, a luggage car (or two) in the end and the sleeping cars of three classes; usually the 1,2 class cars are coupled close to restaurant.
The cars of 1 class ('SV' ?) and 2 class ('kupeiny') have 9 separate compartments with 2 or 4 sleeping shelfs in each. The 3 class cars ('platzkartny') have 54 sleeping places in common volume.
Most of distant trains have their own usual days of week and time when they run. Some of them have their own names; in such trains interior of the wagons is specially designed (with special curtains, carpets etc), some additional services could be offered to passengers, but in the each train there are its own features.
Trains of each category have the numbers from special interval. For example, suburban trains have numbers 6000-6999, 'interurban' - 800-899, fast - 1-170 etc.; numbers are used in pairs (even - odd), the number specifies a direction of the train - coming back, it changes.