There are many different types of flower presses. The simplest one is an old book. Pressing flowers between the pages of the book, or between sheets of paper inserted into the book, and then placing heavy weights on top of the book, works for many types of thin flowers and foliage. This is a good way to begin flower pressing and find out if you like doing it.
I use my homemade press a lot. Here is how to construct it: Go to your nearby home improvement center. Get a piece of peg-board (good for ventilation); make sure you have chosen the thicker kind. Ask them to cut two 12" X 8" pieces for you. The important thing to know is that you do not care about the precise measurement of the boards, but you don't want them to cut through the holes. Make sure you tell the person cutting the board to cut between holes, leaving the outer rows of holes fully intact. Also purchase two packages of foam air conditioning filter (each package of foam can be cut into 4 pieces making a total of eight pieces of foam) and 4 sets of bolts (1/4" X 2") and wing nuts. You will thread a bolt through a hole in each of the four corners of your peg-board. Cut off the corners of the foam air conditioning filter to make room for the bolts. As for lining paper to place your flower on, you can use scratch computer printing paper (or any copier paper). If you would like to smooth the flower press's edges, you can file or sand them. You can also paint the press any color you want. However, these steps are for decoration and will not affect the pressing results.
I also use a Microfleur (a microwave press) for some flowers. Microwave the flowers in short bursts of time. When the flowers are just slightly damp, put them in a regular press overnight to finish. Other microwavable flower presses are also available. An inexpensive way to try the microwave method of flower pressing is by using two heavy-duty pieces of cardboard, sandwiching soft papers with the flowers inside, and securing the stack with heavy duty rubber bands.
The #1 method I use to press flower is by pressing with desiccant board. Desiccant board is about the same thickness of a mat board but it has silica gel embedded inside. Activate it by heating it up in a regular oven at 175ºF for 15-20 minutes while processing flowers for press. I place desiccant board, VIVA brand kitchen towel (with no indentation), flowers, VIVA brand kitchen towel, desiccant board together. If I have more flowers, I just stack them up. When I am done, place the entire stack into a large plastic bag forcing out air and tie the opening. I place this bag on a level surface. Then I place a large board on the top (must be able to cover the board size) and place weight on the top of the board. I often press massive amount of flowers. This is the most effective way for me to press. The Japanese press with cushion is a fancier version compare to desiccant board. The pressing pad consists of sheets of fabric with desiccant embedded wrapped in a non-woven soft cushioning fabric. Using the very thin Japanese pressing paper together, this desiccant press is ideal for pressing materials with a little heavier centers. Activate the Japanese press pads in a microwave oven 2-3 bursts of 30 seconds in high power. Press flower this way: press pad, pressing paper, flower, pressing paper, press pad. You can stake them up. Place the entire stack into a large bag forcing out air and tie the opening. Place the bag on a level surface. Put weight on the same way as pressing with desiccant board above. For difficult to dry flowers, I press with my home made press and then place the press into my large dehydrator (the kind with shelves).