Acoustics
In my opinion, room acoustics is the single biggest factor in determining the quality of your recording. There are two main issues you need to be concerned with. One is how much sound leaks into or out of your studio. The other is the sound of your room.
Leakage
How much you have to be concerned about leakage, or sound coming into your studio, will be determined largely by the noise level of your neighborhood. This will determine the extent to which you will need to go to eliminate this leakage. I'm assuming your studio is in a typical single family home. The main source of leakage to your studio will be from doors and windows. Its good to have double pane windows. If that is not suffiecient, you can add extra glazing or install shutters.
The doors to your studio should be either solid wood or metal. Common hollow-core interior doors will not be enough to keep out the sound from other rooms.
If your studio is in a basement, you may have to treat the upstairs floors to eliminate the noise from people walking. Or, you can just make arrangements to have the upstairs vacant while you are recording. Truthfully, the only time you need to be concerned with outside noise, is when recording vocols or quite accoustic instruments such as accoustic guitars. When recording electric guitars and drums, outside noise is not usually a concern.
Another source of noise is the furnace and air conditioning. I always turn them off while I am recording. Refrigerators are also a source of low frequency noise. Make sure you isolate your studio from this as much as possible.
Reflections
Reflections include reverb, echo and standing waves. Each of these effects the sound of your room. Reflections can be detrimental to your recording. The problem is that sound waves bouncing off the walls, ceiling and floor will return to the microphone. This could simply result in the presence of reverb from the room in your recording. Most likely, this reverb won't sound very good. Another problem caused by reflections is phasing, or cancellation. This is caused by the source sound bouncing off the wall and returning to the microphone out of phase with the original sound. Also, the sound may be in phase in some frequencies and out of phase at other frequencies. This causes some frequencies to be exaggerated and others to decrease and will prevent you from getting that nice full clear sound that you want to have in your recording.
Professional studios usually use special acoustic foam to remove reflections in the mid and high frequencies. In the home studio, you can obtain good results with much less expensive materials. A popular material is "moving blankets" used by moving companies to protect furniture. These can be purchased from Harbor Freight among other places for less that $10 a piece. Another possibility is to lean mattresses against the walls. This works very well. Office dividers used for cubicles also work. You can often find these at used office furniture stores.
Square rooms tend to make the reflection problem even worse. When you're setting up your material you should try to set them up at angles so they are not facing each other.
If you're recording something that produces low frequencies, you may also need to have bass traps. There are many DIY bass trap designs available on the Internet. To determine if you need bass traps. Stand in the corners of your room while the sound is being produced and see if the bass gets louder there. If so, you should install bass traps.