You don't need special equipment for card weaving. I'm using cards I made from normal playing cards and two small clamps, which can easily be attached to a shelf or table.
The cards are easy to make. You need to cut cardboard squares, draw diagonal lines from corner to corner and draw a circle using the point where the lines cross as the center point. The circle should go near the sides of the square. Then you make holes just inside the circle in places where a diagonal line and circle meet. A hole puncher is perfect for making the holes. Finally, round the corners of the cards. The picture below shows the lines, circle, holes and rounding of corners.
I don't remember anymore where I found this piece of information, but it was very useful as I was getting desperate with the first set of cards I made, because they didn't turn correctly. When the holes are placed as described above, the corners of the cards won't snag the threads, provided there is enough tension.
For basics, see Basic Tablet Weaving. That will help you to get started. For more information, you could see Candace Crockett's book Card Weaving. I have found it very useful for getting to know more than just the basic techniques and patterns.
Below is a small video clip of a card weaving project where I'm using sewing thread for making miniature bands for a doll project.