The good thing about an apartment if you are single is that you can bring girls back there without paying an oxranik (security guard) a bribe. Also, it gives you a feeling of freedom and a different taste of former soviet life, right from paying bills and other adventures.
The downside is that an apartment is a lot more expensive and, especially in Moscow, you don't get much bang for your buck. In fact, a one bedroom shithole near the metro will set you back at least 30k rubles (as of 2015).
Demand is always high in Moscow giving landlords a lot of leverage (they don’t care about references and contracts, just getting their money). You get some real bad landlords and when times are tough economically, rent can jump up and down. I have an article on shitty landlords here - for your reading pleasure.
If you find your apartment via a real estate agent, you can expect to pay a deposit (one month rent), agent’s fee (normally 50-100% of one month rent) and one month rent upfront.
The best way to find an apartment or roommate, in my opinion, in on expat.ru, flatmates.ru, redtape.ru or cian.ru. I always used expat.ru and had no problems, also this way you avoid the big financial hit.
You will not be able to bring people back that are not students without paying a bribe - normally a couple of hundred roubles. Sometimes the oxranik may not accept bribes (this is rare, but annoying when it happens).
Russian dorm administration treats you like a child, some are worse than others, but one place I lived in the administrator would conduct inspections and threaten to evict you if your room wasn't clean to her outrageous standards. That bullshit gets old fast, trust me.
The rooms can be hit or miss, below is a picture of my room in the main building of MGU (very nice on the outside) and below that is my room I shared with a Chinese guy in another MGU dorm (DSV). As you can see, the Radisson they were not:
The MGU main building presidential suit
Then DSV (below)
(below, another room in DSV, but a better one)
--> If you are going to study with an MGU program, I recommend DSV or the main building - both have plenty of action going on and plenty of chances to practice your Russian, party and hone your seduction techniques. Whatever you do, don't chose Шабловка. You can't bribe anyone in, there are no Russians there and if you are making any noise after 11 you get told off by administration. Also, you are not allowed out after 12, or you get a warning and, again, threatened with eviction. It's worse than living at home and your Russian wont improve much, but the rooms are quite clean and of a decent standard.
Sleeping like a disgusting alcoholic Moldovan baby...
1) You need registration. You should get registered within 5 working days of arrival by giving your migration card to the place that is registering you. Registration is valid for the length of your visa. If you leave, cross the boarder etc, you need to re-register.
2) If you study, you should be able to get registration for the whole duration of the study visa without leaving.
3) If you are in a hotel, they will register you.
4) When you buy a work permit, you will get one year registration with it in most cases.
5) As another general rule, after your registration is up, you need to leave the country. You just need to effectively cross the boarder to get a new migration card. You can do this by taking a cheap train ride, for example, to Riga and coming straight back. It's a pain, but sometimes necessary.
6) If you rent an