You need to build an isolated 'room within room'because you are dealing with 3 main issues.
1. Acoustic sound waves travelling through air
2. Transmission of sound waves through solid structures
3. The performance acoustics in the room you finally construct
a)make sure your new framework is isolated from the original structure by neoprene strips or if on a tight budget any rubber that comes your way (try scrap yard cars for matting etc) it's not to any code standard but it will work... Pay attention to the floor, it needs a neoprene 'lip' round it's sides before it touches any wall. If you can allow for 'dead' air space round the outer side of the frame so much the better.
b) fill the framed walls with RW3 rock wool (or something like it but more Eco friendly!)
c) use a minimum of 2 layers of plasterboard (of 2 diff thicknesses) screw the first lot of plasterboard to frame. SEAL all edges, then glue 2nd layer of board to the first in a staggered fashion eg don't have 2 sets of edges lined up together. If either set is sitting directly on your floor, isolate them with neoprene or similar. Seal all the edges like your life depends on it.
d) you need a similar approach to the ceiling except now gravity works against you!
e) make the door as dense/heavy as you can and find a some simple DIY rubber draught proofed to run round the frame edge.
Consider that if you leave an air gap the sound will leak, it's incredible what will spill through just a keyhole! So after you've isolated and made it airtight your going to need to breathe.... And if yr drumming it's going to get hot fast!
Look into fans and baffles or silencers for the ducting. Pay attention to how/where the pipes enter and exit. Same goes for power cables.
When you've done all that listen to how the space performs and treat accordingly. You can help yourself here if you used good room dimensions to start with. As a basic rule of thumb try and avoid an absolute cube shape eg 10'x10'x10' and try and build a little 'off' eg no wall or floor to ceiling is absolutely parallel. Even a few inches diff will help prevent a build up of standing waves inside the room...
Pay attention to details and you will be rewarded. It will not be absolutely soundproof because of the space your starting with but if done right it will be EFFECTIVE, you get to keep your friends,neighbors and your soul.Most of all good luck and have good courage when the strength starts to fail. Laters.