Your house may already have a perfectly decent booth for recording vocals. A closet, a bathroom, a pantry or a shower stall all have potential. You'll want to find a room that's close enough to your recording rig to run cables, big enough to fit a person and a mike stand, and has minimal ambient noise (no computers, clocks, aquariums, leaky faucets or air conditioners).
Don't worry about getting yelled at by your wife or mom for "ruining" the bathroom; the installation will be temporary.
If you don't have a room near your studio that will work as a vocal booth, you may be able to section something off using scrap pieces of wood and drywall, or by hanging layers of heavy blankets and materials to create a booth-like partition. Even large appliance boxes can serve as a vocal booths--after all, you're a do-it-yourselfer.
Begin hanging soft, porous materials on the walls and other surfaces. Thick blankets, carpet scraps, packing materials and foam mattress pads are all good choices. The idea here is to supply the environment with materials that kill echoes. Obviously, special-order materials from a studio supplier work the best to kill echoes at all frequencies, but they are often beyond a "do-it-yourself" budget. If you do have a budget to work with, and a space to use for a permanent installation, you can order kits of studio foam for around $100.
There need not be any specific rhyme or reason to the placement of materials. It should be arbitrary but even. As a general rule, the more hard surfaces you cover and the wider the variety of materials you use, the deader your sound will be.
If your vocal booth is going to be temporary, use rope and removable tape to hang materials.
You'll also want to try to limit the number of parallel surfaces in the room. Parallel surfaces, in theory, cause echoes to infinitely bounce back and forth at a constant rate of speed, which can give your vocals a harsh, unnatural presence. Obviously this is easier said than done when working in a closet or bathroom--walls tend to be built at 90-degree angles from one another. Simple ways to limit parallel surfaces are to lean tall scraps of cardboard or drywall in one or more corners, prop the door open slightly so that it is not parallel to the opposite wall, and do not have the singer or the microphone facing perpendicular to any wall.
The biggest misconception in creating a space to record vocals is that a vocal booth is supposed to be soundproof. The goals are to create a space with a flat frequency response and to reduce echoes. Soundproofing really has nothing to do with it (although you'll naturally want your booth to help reduce the presence of external noise sources.)
Creating a truly soundproof booth would essentially require building a room inside of a room, and using several layers of different materials in the walls. Such a booth is really not within the scope of a temporary, low-budget vocal booth project. An advanced recording booth that kills all outside sound is known as an "isolation booth."