A brief introduction to soundproofing
Soundproofing is also known as 'sound insulation' or 'sound isolation'. No room is completely soundproof, so the term is a little bit misleading, but it's the most commonly used term so we'll continue to use it here.
Let's start from the point of view that there is background noise leaking into your room, perhaps from traffic outside. Firstly, does it matter?
There are some areas of recording where background noise is a killer. Foley sound effects for film and television is the very most demanding area. This is where foley (named for Jack Foley - the inventor of the method) artists add noises such as the rattle of keys, the rustle of clothing, the creak of a leather armchair when someone sits in it, while watching the picture live on a screen. They actually rattle, rustle and sit - they create the sounds of real life. Since many of these sounds are very quiet, the level of background noise has to be extremely low to do this successfully. It is so demanding in terms of soundproofing that it would be almost impossible to set up a foley studio at home that was capable of professional work, at least at a reasonable cost.
Speech is demanding too. Imagine listening to an audio book and there is traffic noise in the background. The gaps between words allow any background noise to come through very clearly. Yes, there are noise reduction plug-ins, but this isn't the way the professionals work. Professionals will only turn to noise reduction plug-ins if they really have to. The results are never as good, and it slows down the working process.
If you were recording a classical string quartet, this would show up any background noise too as the instruments are fairly quiet themselves. But...
If you were recording a heavy metal rock bank in your home studio, background noise wouldn't be a problem at all! The problem would be the amount of annoyance you were causing to your neighbors.
Another type of music where background noise isn't so much of a problem is electronic music, such as dance music. If no microphones are involved in the recording process, then there is no way for acoustic background noise to get in.
It is worth saying however that you have to be able to monitor your recording with a reasonably low level of background noise. If you are trying to judge the quality of your recording, even heavy rock or electronic music, against a background of traffic noise, clearly your judgment will be impaired.
How to achieve good soundproofing
The first thing to realize is that you will never achieve perfect soundproofing. Not unless you have a budget of tens of thousands of dollars. But small improvements in soundproofing can result in impressive gains in the quality of your recordings. And some of these improvements cost nothing.
The first thing you should do is to try and get away from the source of the noise. So if traffic noise is coming in from a road on one side of your apartment or house, then set up your home recording studio on the other side. Find the quietest place in the house to set up your studio. Or at least use that as your recording area when you need to record vocals or acoustic instruments. Another option is to record when the traffic is quiet - in the middle of the night, if need be, for an important project.
The next cheapest tactic is to work out where the noise is getting in. Nine times out of ten this will be the window. The glass will be thin and the panes that open poorly sealed. Improving the seals and having secondary double glazing installed will improve the soundproofing qualities of the window enormously for a reasonable cost. Two layers of 6 mm glass can provide very impressive results.
If you are still troubled by background noise at this point, then the next least expensive option is to buy or construct a booth. Since a vocal booth, for instance, doesn't have to be big, it's a lot easier to build one with good soundproofing than it is to try and soundproof the entire room.
But what if you do want to soundproof the entire room? Well unfortunately this is where you can spend a lot of money and end up being dissatisfied with the results. Ideally you would hire professionals to do the work. Or you can learn the principles of soundproofing. It's a fact that materials that are first-class for soundproofing are available quite cheaply from builders' merchants. But there's a lot to learn first, to be sure of getting good results.
One more point... A room that is soundproof is also air-proof. You will need ventilation to bring in fresh air from outside.