The first step is the simplest, just try and choose a room to drum in, that is the furthest away from other living areas in the house and from your neighbors.
If you still live at home, talk to your parents. Maybe they would let you use the garage to practice in. All you would need is a small heater.
If one of your siblings has a room, more out of the way, ask whether you can trade. This should keep everyone happy.
Talk to your family about sound proofing the room. Although it is very expensive to professionally sound proof a room, there are steps you could take to reduce noise.
If you are allowed to use the garage, that would be best, as sound proofing isn’t always pretty.
Talk about what budget is available for sound proofing and look at your options from there.
Here are some options that you can use for sound proofing:
Acoustical foam can be bought from music and hardware shops. This is rather expensive, but when attached to ceilings and walls does a great job at sound proofing.
Extra insulation will also help.
Carpeting will help reduce sound waves. Generally speaking, the rougher textured carpets will absorb more sound waves.
Egg crate mattress pads also absorb sound and can be attached to walls.
Fabric furniture pads are often used for sound proofing and are available from furniture shops. Try to avoid the flimsy furniture pads, as these will not work as well.
Add a thick rug to hard wood floors.
Thick rubber mats, or gym mats can be used to stop vibrations, under your drums.
Ask your local movie theatres whether you can buy used draping. This is a very thick material and works very well. Used products are also a lot cheaper.
It is very important to install a smoke alarm and make sure you never use candles in your drum room. Some of the sound proofing equipment would catch fire easily and could end in disaster. However with care, this can easily be avoided.
Keep your room clean and dust free.
If you are buying used materials, you may want to hang them outside for several hours, to get rid of any odor.