You don't need many materials to make this but you do need:
- 2by4 inch lumber
- Soundproofing foam
Firstly the size of your booth is your initial decision to make. 4ft by 4ft is fine as a start. Place frame in the vocal booth from the bottom up to the ceiling. Allow a space in one of the custom walls so you can go in and out.
Apply some drywall to the exterior of the walls and nail into place. Fill the area inside with studs and then apply insulation and hand drywall inside.
Now that you have framed the door, hang it, in an ideal world the door will have at least a double pane window. It's important that the fit of the door is tight to ensure the maximum amount of sound to be kept in the booth.
Drill holes in the wall for the microphone and headphones and cords, seal the openings using caulk. Use the same technique for a ventilation fan.
Use soundproofing foam to cover the walls and ceiling area of the booth to trap the sound.
Now you are ready to connect your equipment together, experimenting with mic position for best results.