A real simple one can be made from cardboard and newspapers. The size depends on how big your specimens are, you'd best start small so cut the cardboard and newspaper into 4"X 4" or 6X6, squares. Now make sandwiches, one piece of cardboard, 2 pieces of newspaper, the plant, 2 more newspapers and 1 more cardboard. Make a complete sandwich for each specimen. Stack the sandwiches up and put a few rubberbands around the whole thing and put it in a cool dry place for a few days. An improvement would be to put a 3/4" or thicker board the same size as the cardboard on the top and bottom, use heavy rubberbands or pile bricks on it. You can use more newspaper too but not so much that it gets cushony and lets the plant bend, you want them to stay flat. You can put plain white paper between the plant and newspaper if you're worried about ink transfer. You can also use paper towels but use a newspaper to separate it from the plant.

A simple method for constructing a plant press involves the use of two 12" x 18" sheets of 1/4" plywood, a number of sheets of corrugated cardboard roughly the same dimensions as the plywood, 2 lengths of strap with buckles that can be cinched tight, and a newspaper. Place one sheet of plywood on a level surface. Add a sheet of cardboard on top of the plywood. Put one sheet of newsprint on the cardboard, carefully arrange your plant specimen on half the sheet, cover with the other half, and then place another sheet of cardboard on this. Repeat for as many specimens as you have and top the whole thing off with the second sheet of plywood. When the press is assembled, wrap the straps around it and tighten them. Pile some books on the press or stand on it to flatten out the plants. Retighten the straps after a few hours if necessary. Allow the plants to dry in a warm, well-ventilated area for a few days. Once dry, keep the specimens in the newspaper until you are ready to mount them. Special precautions need to be taken when pressing succulents, thick woody stems and roots, very large leaves, very small plants, large fleshy structures, very spiny plants, and submersed aquatic plants. Always remember to adequately label every specimen you collect!