Taking the time to build a recording studio in your garage is a great way to create an environment that will foster your creativity. There are just a few issues you need to consider when designing your studio.
Soundproofing is paramount, both for your sake and your neighbor's. Total isolation from the outside world is unlikely given the size of the average garage, but you can lower sound transmission significantly. First, to prevent airborne transmission of sounds into or out of your studio, ensure that there are no air leaks in any joints anywhere. Add extra insulation, caulking, or both around electrical outlets, light fixtures, windows, and doors. Make especially sure the door that connects your garage to your house is solid, heavy, and seals completely when closed.
For more complete soundproofing you can add another layer of drywall over the existing layer - the added mass will lower sound transmission without taking up too much space. You could also float an additional wall over the existing walls, using resilient channels or Z-bars, but that is generally beyond the scope of a garage studio conversion.
Now that you have your garage sealed up as tight as it should be, you're probably wondering how long you will be able to survive without air! Conventional heating and cooling systems are giant holes in your otherwise airtight studio, and if your garage has an AC duct, you will probably want to plug it up. Installing professional studio-grade AC is prohibitively expensive, and the typical in-wall AC system is prohibitively noisy, but there is another option - the split system. The fan part is located inside the room, and the noisy compressor is located outside. You will still want to open a window now and then to let the fresh air in, but you will stay comfortable and your sounds will stay inside.
The next thing you will want to consider is your control room and its relationship to your sound stage. How you build this depends entirely on how you expect to use your studio. Recording other musicians means you will probably want to build a control room isolated from the sound stage so that you can better listen to what the microphone is capturing. Given the geometry of the average garage, you will probably want to build your control room in one corner. Dedicate about a quarter of your available space to the control room, and leave the rest to the sound stage.
The same isolation techniques will apply here as apply to your overall space. If you are just recording yourself, or if your production is primarily dependent on electronic instruments, a separate control room is not only unnecessary and may actually be detrimental to the creative process of recording.
Once you have finished with the building, finishing, and painting, you will want to address your studio's acoustics. When building a studio from the ground up, the acoustic design is paramount. The lengths and angles of walls, the height of the ceilings, even the materials used in construction are all critical. But when retrofitting a garage, our options are limited so it is best to make do with what we have, and make it sound as good as possible.
The most noticeable artifact of a small room will be standing waves. Standing waves are caused by sound bouncing back and forth between two parallel surfaces - i.e., facing walls - producing peaks and valleys in the audible frequency spectrum. You can hear these easily when you clap your hands in an empty room, or hit those operatic notes in the shower. While it might invigorate your morning routine, it's not so desirable in the studio, so we want to tame those.
That reverberant sound in an empty room is the higher frequency sounds bouncing around walls and windows, called "flutter echo." To tame this, I use acoustic foam panels that absorb higher frequencies on the walls, and heavy curtains on windows with lots of material to fold up. I don't like my rooms to sound totally dead, so I treat only one side of parallel walls with absorbent material, either by alternate checkerboard patterns on each wall in the case of foam panels, or by a plain wall on the opposite side of a curtained window.
Another way to tame flutter echo is with diffusion - the kind you get with a bookshelf filled with different-sized books. The sound hits that complex surface, and bounces all different directions, diffusing the sound but leaving your room sounding more open. Instead of a plain wall on the other side of a curtained wall, a bookcase works very well. There are also acoustic tile manufacturers who build diffusion modules using precise mathematical calculations, but for a garage studio it can be expensive overkill, money better spent on a good microphone or preamp.
There are pros and cons to carpeting the floor, as carpet alone will not do much to prevent anything other than high frequency flutter echo, and some feel it only deadens the sound of acoustic instruments. I personally like having carpet underfoot, rather than cement, so I use a heavy pad and plush carpet to lower the frequencies that are affected. I also have an office chair mat that I sometimes set down before recording acoustic guitars.
Converting your garage into a recording studio is a lot of work, a lot of fun, and if you are patient and careful, you will have something that'll give you great pride, and serve as comfortable space that will give your muse space to expand. For more information on how to build a recording studio in your garage, be sure to spend a lot of time on the internet, and by all means pick a copy of F. Alton Everest's book, Master Handbook of Acoustics which includes invaluable theory, practical plans, and real-world examples.