Not certain what kind of reflector you want to build. The little ones in speedlites are just white plastic, but a much larger size of it would be too flexible and difficult to use.
Any material that reflects or absorbs light (depending on your need) will work, but if not black (absorbs light) or white (reflects light) it's color will bleed into the reflection. It should also have a flat (non-glossy) surface. In my studio I keep sheets of black and white foam core board, (purchased from a stationery or art supply store) and use it to reflect (bend) or block (absorb) light. The size will be decided by the need. Use whatever is necessary to position and hold it in place for your photo shoot. Having black and white Gaffer Tape on hand helps with this, but for just a one light setup for a portrait, I frequently just get the light positioned to light one side of the face. Then I hold a piece of white foam core board out and in position with one hand, while operating the camera with the other. When positioned correctly the light from the one source will be reflected off of it to light (at a lower level) the darker side of the subject's face. There are many Youtube videos that show photographers using reflectors or flags (the black light absorbing version of a reflector). Bigger is usually better, in many cases. Hard light becomes softer when reflected off a white surface. You can even reflect off a wall or ceiling if it is white. Avoid trying this with colored walls or ceiling, because the surface color will bleed into your shot and change the result. Foam core board is low cost and easy to cut to size. You can even make shapes from it using the appropriate color Gaffer Tape.
Then there is the alternative - Photography reflectors. These are usually made to fold easily because of a spring wire perimeter. Some have zip on covers so their color can be changed. Though quite handy for many shots, they are more expensive, and cannot always fit the need. I keep several different sizes of these on hand in my studio as well as the stock of foam core board.
I have also made very large reflectors/flags of covered sheet foam building material. I painted one side flat white and the other side flat black. Then made a plywood stand, a base with two vertical pieces of plywood with a slot between them for the foam panel and painted it black / white too. These become portable partitions to place in my studio to act as reflecting / flagging walls for certain shots.
Whenever you use a reflector, the angle of the light hitting the reflector will always equal the inverse angle of reflection of the light leaving the reflector. It's sort-of a mirror, but of a lower quality. in use, practice will teach you all that is needed.
Charley
