Decide on size. Consider the size of the instruments you want to record in the isolation booth. If you just need a booth for vocals, the isolation booth does not have to be large. However, if you plan to record large guitar amps or keyboards in the isolation booth, you will need a larger space. In general, a smaller room will sound deader and a larger room will sound livelier.
Choose your shape. Parallel walls can introduce problems with standing waves, so avoid parallel surfaces as much as possible. Use wide angled corners and consider non-rectangular shapes like a pentagon or hexagon. Be sure that the shape you choose doesn't constrict the size of the room.
Use acoustically isolating materials. While standard drywall provides some acoustic isolation, there are specialty brands of drywall that will more drastically reduce the transfer of sound in or out of the isolation booth. You can also use double layers of drywall. Use caulk instead of screws or nails when practical. Be sure to seal all joints. Use dense insulation if possible.
Stagger your studs. Instead of framing the walls for your isolation booth with standard two-by-fours for the base and the studs, use a two-by-six for the base and two-by-fours for the studs. Then alternate which side of the two-by-six each stud is on. This will decouple the inside wall from the outside wall, making it more difficult for sound to transfer through both walls.
Wire your booth for power and audio connections. If you plan on using electronic instruments inside your isolation booth, you need to have power outlets. Also if you want to use a microphone in the booth, you need an XLR connection. Wiring these connections is much easier while the walls are being constructed.
Mount a door and windows. The door is often the weakest part of an isolation booth. Use a heavy, solid core door to prevent sound leakage. Make sure you use a good doorjamb and use weather stripping to seal the top, bottom and edges of the door as necessary. If you choose to install a window, be sure that it is secured as tightly as possible to avoid rattle. Use two panes of glass for further isolation if possible.