I was at a training this summer where we pressed plants using a homemade press (second picture). I thought that was pretty cool and certainly something a teacher could make using two pieces of cut plywood and pieces of cardboard in between. The plants/flowers were put between newspaper and put on a cardboard piece and then stacked with other specimens between the plywood. The instructor said it take about 2 weeks to dry out. The whole thing was cinched with luggage straps.
They also showed us how to make a mini flower press (first picture) using cardboard and index cards. Obviously these would be smaller specimens and the professor suggested putting wax paper between the layers. The rubber bands would be used to secure the "press".