When looking at soundproofing a room, many things can be done. Some of them are simple, while others take a bit of skill. If you are not that handy of a person, perhaps hiring a professional contractor to do this sort of work is best. However, if you use a hammer and nails and have a drill, some can be done by the homeowner, as some sets are super simple.
First, let's look at the door. Are there any significant gaps that you see? These gaps are certainly letting in sound as well as letting out any noise. Take a look at the bottom; is there a gap? If there are large gaps where you can install a commercial grade door sweep that will help close this gap and keep the sound down.
Cover Hard Surfaces
Hard surfaces bounce sound off of them. Things such as walls, ceilings, and floors are where the sound starts to bounce. By adding soft surfaces to the room, it will help as well. Although this won't soundproof it entirely, it will help with rugs and pillows as well. This is great for the rooms that are echo chambers.
Add Foam
For better soundproofing, there will need to be panels hung on the walls. These panels can be something as simple as foam sheets to Acoustic panels. There are even companies that make unique doors that can retract when not in use. This is perfect for a bedroom door where you are looking for some privacy. There are soundproof window treatments that can be used as well. These window treatments roll up when not in use, but roll down when you are trying to sleep, and your annoying neighbor cannot stop mowing the lawn.
There are also window inserts that can be put in from the inside to make the windows more soundproof. This is also great for energy efficiency as well. These simply slide in the window's opening with rubber on both sides.
For the more elaborate types of soundproofing such as thicker insulation in the walls and ceiling with the soundproofing panels on the walls and ceiling will help. Of course, this will change the structure of the room and is a bit more permanent. However, if you are looking to soundproof a room so that you don't disturb others as you practice your band, this is a great option. There are many different sorts of soundproof insulation out there to choose from.
Thicken up the Walls
Or if you don't want to change the structure of your home permanently. Putting bookshelves on the wall that you are looking to soundproof helps as well. The books will absorb the sounds and is a temporary solution. Or you could hang the soundproofing up on the walls in sheets to get a bit of a thicker wall, and then add the bookshelf.
For items that might rattle such as hard speakers on a hard surface, why not put them on a bit of foam to help absorb the sound and keep them from shaking.
And, there is always the possibility of putting up a double layer of drywall or sheetrock. This method is called decoupling. If you go this route, getting a dampening compound between the layers will help.