There isn't really any enforcement of copyright laws at all. Well, I guess that isn't completely true. It looks like Microsoft got in with someone and so most Microsoft products are legal copies. However, most everything else is pirated over and over.
How can you tell if the movie/cd/software that you are looking at is pirated or a legal version? Price of course. Good quality pirated DVDs are around 100 rubles or just over $3. You can expect to pay about $15 for a legal version of the film. You can find even cheaper films as well but the quality is very lacking and leaves a lot to be desired.
A CD will usually go for about $2 and sometimes you will find CDs of MP3s from an artist for the same price (there is usually about 100 songs on a cd like this). You can expect to pay about $5 for a pirated computer game. Xbox and Playstation aren't really popular in Russia so I don't think I've seen any "illegal" copies before.
DVDs, CDs, and computer games for sale on the rionok.
DVDs and computer games for sale in Russia.
Shelves of pirated DVDs for sale inside a store in Russia.
Like I said, I am not sure if there are copyright laws in Russia or what but they aren't enforced if there are. If you do decide to buy films in Russia though, whether official or unofficial copies, you will want to make sure that you have the correct region encoding or else you will be out of luck.
Also, Russian websites also have lots of pirated movies, cds, and games that can be downloaded. However you have to know Russian on most any of these sites. A lot of them are locked down to Russia only as well (for good reason).
One other thing that isn't unique to Russia but I find interesting is that ratings aren't given to films. No R, PG-13, PG, G rated films. Really there isn't any rating or way to know what the film contains without doing some research on your own. It's pretty tough to explain to someone the rating system (believe me since I tried to do it several times).