[Al Skierkiewicz]

Filter out what has already been printed here. The only way to contain sound is add mass between the source and everything else. The amount you want to spend and the area in which you work are the determining factors. If you want to play drums while everyone in your house sleeps, you are going to have to spend some money. If you just want to practice while everyone else is watching TV that will cost you less. Several books are availabe at the library, I recommend F. Alton Everest and his books on studio design.
You are dealing with two types of sound transmission. One is through the air and the other is structure borne. To kill the first, you need a lot of mass, double or triple drywall walls and ceiling, lead sheeting, sand filled block, concrete, etc. The second requires you to break the structure to eleiminate the path between what's inside and what's outside. The only way to do that is to build a room within a room. You start by floating a floor (isolators, rubber sheeting etc.) then build the walls and ceiling on the floating the floor. This is what most studios do. Everywhere that the structures must meet, there needs to be a flexible joint.
For a simple practice room in a basement, build the walls on the concrete floor but not touching any of the building. Use 2x6 studs on 16" centers for rigidity. Add a ceiling to the walls that does not touch the building. Two sheets of 1/2 - 5/8" drywall inside the room (walls and ceiling) and one sheet of drywall outside the room. Caulk the joints with the floor with butyl rubber so there is no air leaks. Do this for each layer and overlap drywall so there is no common joint. You can add insulation to the walls but it adds little to the transmission loss. (remember mass is what kills the transmission so even rigid fiberglass is only a pound or two per square foot compard to the weight of drywall.) Add a heavy, solid core door with rubber seals around the sides and top and a drop seal at the threshold. Any intrusion (air conditioning, electrical) must be sealed (caulk) and isolated as well. Make the duct a nice long run with a few bends, fully lined with fiberglass, so that no sounds travels out through the duct. Wide, short duct is better than square cross sections or round.
If you do the work yourself, you maybe looking at $500-$1000 in materials. Add absoption (foam, carpet, heavy drape) as you feel you need, to make the room comfortable to be in.