I have an aversion to reading directions and doing things the "right" way. Sometimes this can lead to innovations and interesting discoveries and sometimes it gets in my way. And it's probably the reason that my plant press still looks like this! Two pieces of wood, the same size, one on the bottom one on the top, layers of cardboard and paper, and weighted with two giant dictionaries. It actually works really well! I also stick small specimen into the books to press (in paper).
Ideally, if you were making a proper plant press, you would have two pieces of wooden board, equal size, latticed or at least with holes cut in them for ventilation. Pieces of cardboard the same size as the boards. Absorbent paper, such as paper towels or blotter paper, newspaper to fold the specimen in, and straps to cinch the press closed tightly. If you have a fleshier plant with more water in it you will need to change the blotting paper out after a day or two. I often have large pieces of glassene left over from shipping or transporting artwork and I reuse it in my plant press.
How you arrange the plant before you press it is also something to consider. You can adjust the shape it will end up in by spreading leaves and flattening it in a particular way.
When you choose which plants to press, don't rule out weeds! Weeds make some of the best specimen. Below you can see Dandelions which create really interesting shapes. Another favorite of mine is Vetch. Queen Anne's Lace makes another fabulous pressed plant. So keep your eye out for all the great weeds around!!