First of all, you want to work on the doors and windows of the room, as that is where most sound will escape. Properly sealing the doors and covering up the windows will make a big difference.

After that you need to improve the soundproofing of the walls. Best bet is to effectively build a smaller room within your existing room. Stud walls with an air gap will cut down the sound going through the walls. For best results though you dont want to have the new wall attached to the old wall, as the sound will just travel straight through the studs. You need a the old wall, an air gap, then the new wall. That will cut down the sound transmitted considerably.

Personally I recommend moving somewhere where your neighbours make considerably more noise than you ever will, then you can just completely forget any ideas about soundproofing and turn everything up to full without worries.