Moscow is on a pretty late timetable.
A typical night would be to get together for pre-party drinks at one of the many DJ bars at around 22:00. Then you start moving in the direction of the club after midnight.
The nightclubs open at 10 or 11. Some clubs get fullest around 1:00 and start to get empty around 3:00, while others don't get full until later and stay packed until 5 or 6.
Since you don't have to pay to go to most of the best clubs, people will often start at one club and move on to another one. Instead of a door charge, the discos have "face control", where there's someone at the door who only lets in people he thinks are cool. The key is to be a regular clubber so that they know you and let you in.
Most clubs close at 7 or 8, but if you have a lot of stamina, there are a few nightclubs that stay open until the afternoon on Saturday and Sunday. If you go there at 1am, there is nobody! If you go at 6am, they are totally packed.
The great thing about this city is that it's 24 hours. There's no restrictions on alcohol sales or opening hours. So, if you get hungry at 6am or just want to go with your friends somewhere to relax with a drink after the club, there are 24 hour restaurants, DJ bars and cafes where a lot of club people go after-party.
The best thing is, most of the interesting places to go are concentrated in the center so at night you're never more than a 15 minute taxi ride to a good selection of new destinations (and taxis are about the only cheap thing in this city!).