There are several thing you can do but it depends on your goals. Do you want to keep other rooms in the house quiet? Are you trying to get a better recording? Do you want to tear out walls and rebuild? Are you on a shoestring budget?
My friend and I soundproofed his basement on a shoestring budget in order to get better sound during recording sessions. We were not concerned with sound traveling upstairs. We wanted to cut down the standing waves from high power guitar amps and reduce the vibrations caused by drums. We started with the worst possible room. Cement block walls and cement floors cause all kinds of reflective sound waves.
What we did was talk with the local flooring and rug guys. We found that they had a contract with the some large townhouse and apartment owners. Tey were constantly replacing a standard brown carpeting that was sometimes less than a year old. So we got the crew to tip us off when they were ripping out almost new carpeting. Two layers of carpeting on the floor and two layers on the walls did the trick. We hung one layer next to the walls and another a few inches away. It was a great free solution, and the results were exactly what we were looking for. Remember that rugs on the walls may present a fire hazzard but most today are fire retardant.
This solution wouldn't work if your are looking to build a classical recital room to invite stuffy people in penguin suits over. It depends on what you want and how much you want to spend.