this site is the best for this sort of thing, I am a member there and could not have soundproofed my garage without it.
http://johnlsayers.com/phpBB2/index.php
in order of preference these are your basic options in a nutshell.
ideally you would build a new room just inside your current space, with separate walls and ceiling, with multiple layers of drywall on the inside (room side) surface of the new walls and ceiling only. Insulated fully as well. Do not drywall both sides of your new wall as that will actually be worse than putting all the drywall on the inside (toward the room).
Second best would be to build just a new second ceiling below your current ceiling not touching the first, with several layers of drywall on it (facing into the room only) and insulation between. new ceiling could be supported by existing basement walls just about an inch below your current ceiling, using metal hangers for example.
Either one of these options will cost you headroom since you will need at least 2x6 inch or greater new joists depending on span distance.
Third best, but which will save your headroom, attach several layers of drywall (somewhat) directly to the existing rafters but with "resilient channel" holding them up ... that is a long metal channel that acts as a kind of spring between the new drywall and the rafters which decreases sound transmission. make sure to get proper RC not "hat" channel. So the drywall is not directly attached to the joists but actually to the channel. This way you will only lose about 3 inches depending on how much drywall you use.
of course you have to make sure the rafers can support the extra weight.
also make sure as i said to fully insulate between. and caulk any gaps.
hope that helps.