Acquire the necessary materials to soundproof your room. Almost everything you need can be found at the local carpet store. Most carpet stores have returns and plenty of scraps laying around that they plan to throw out and are happy to give them away for free. Call around and find someone who is willing to donate to your cause. You will need to ask for carpet padding, carpet scraps and, if possible, cardboard boxes.
Tack flat cardboard boxes to every square inch of the wall. This will provide some soundproofing but also will allow you to tack the carpet padding easier.
Tack carpet padding to the boxes, making sure to cover all of the area as best you can. This padding will add a lot of soundproofing to the room.
Add the carpet to the padding. Make sure you use plenty of staples for the carpet due to the heaviness of the material. This layer will muffle the sound even more.
Stuff as much carpet padding into the windows as you can. Try and cover as much of the window as possible. Cover the window in the same method as above: cardboard, padding and carpet scraps. If you are in a situation where the window cannot be covered, a mattress will work just as well.
Go outside and have a friend play the drums loudly. You should notice a very big difference in the decibel level.