The most available large sheet material is corrugated cardboard.

If you have a single layer sheet, you should first glue at least another single layer sheet on top of it to make it more stable. Rotate one of the sheets by 90° so that the "grain directions" of the layers cross each other. Like plywood.

For the reflective surfaces:

• White paper provides a nice reflective surface.
• To get a stronger reflector, you can also try aluminium foil (often called "tin foil").
• There is a product available for first aid and rescue situations that's a foil with a silver and a golden reflective side. To keep people cold or warm. This is one source for a golden reflective surface. Which gives warm light which can produce great looking portraits.
• Last but not least, there's black paper which provides the opposite effect of white paper. This is often called a flag. This is handy if you want to pull the dark side of your subject even further into darkness to get very dramatic results. It also helps to prevent light spill or reduce harsh highlights.

These are 4 surfaces. You could make 2 cardboard sheets and get all the different surfaces with one on each side. Or make 4 reflectors with only one surface each if you want to use them together at the same time.

To get the surfaces on the cardboard, use double sided tape. Regular paper glues will not dry under air tight foils. Tape is very convenient to work with for such large surfaces.

If you need something that's more portable, create a hinge in the middle of the cardboard to fold it.