Drums are loud. And few if any neighbours would recommend living beside a drummer who practices a lot. So what is a poor, motivated drummer to do? Rent a practice hall? Good idea, but not convenient and not cheap. Just hope the neighbours are OK with it? Ya, I’ve tried that ... pretty risky. Maybe you can fit up a practice room that keeps the sound inside. That would be ideal. It’s also nearly impossible to achieve, but with a bit of time and investment, you can come close enough.
Sound travels through the air. It also travels through solid objects. And although it’s impossible to eliminate these conduits from you practice environment, there are techniques you can apply to minimize sound transmission.
When I rebuilt our basement, I set aside one room to be my practice studio. I then packed all of the framing with sound-proofing insulation bats -- even the ceiling. I doubled up on the bats as much as possible on the walls that faced the outside.
For the ceiling I used slotted metal lathing. This type of lathing hangs off the joists slightly and adds some acoustical isolation. When the drywall is attached, it can still vibrate, but it doesn't transfer the vibration to the joists very well.
No need to do anything to the concrete floor, but had it been an upstairs room, I'd have put down a subflooring of acoustic foam or micro balloon insulating board, then subflooring, then a carpet or two.
Once the room was dry-walled and taped, and wall-to-wall carpet installed, I tested it and the result was good. You have to stand right outside the house in order to hear the drums. Inside it’s still quite audible, but keep in mind, a drummer lives here. So far no complaints.
To cut down on resonance inside the room, I got some simple Mexican-style rugs from a thrift store. I stapled one to the wall just in front of my drum set and draped another over a blanket rack. I'd been thinking of using office acoustic panels, but they're large, cumbersome, and a bit expensive. The rug rack works just as well, is easy to move about, and looks pretty cool.
That’s a fairly basic solution and it didn't cost much to execute. There are some very good articles on-line that can give you some other tips.