Ok here's the basic idea: in order to turn the raw material into yarn the wheel needs to perform two functions: twist the yarn and wind it onto the bobbin. We want to take a bunch of hairs and make them stick together in a long string and we do this by twisting them together so that it is difficult for them to slide apart. We also want to wind the yarn onto the bobbin as we twist it so that we can produce lots of it.
My wheel is called a double drive wheel which means that the drive band goes around the whorl and then pulley on the end of the bobbin. See the photo below.

I pump the footman which turns the big wheel which makes the drive band go around. The drive band turns the pulley on the outside (called the whorl) which turns the axle which is connected to the flyer. The drive band also turns the pulley on the inside which is attached to the bobbin which spins on the axle (which is being turned by the whorl). The yarn is tied to the bobbin which means that as the bobbin turns the yarn is twisted. The flyer is also turning around the bobbin which winds the yarn onto the bobbin as it is being twisted. Note the difference in the sizes of the two pulleys - the larger one (the whorl) makes the flyer spin slower so that there is time for the yarn to be twisted before it is wound onto the spool.

I'm still working out how to get some action shots but hopefully this gives you a basic idea. I forgot to mention that there is a hole in the end of the axle called the orifice. The yarn feeds through the orifice, then through a hole in the flyer and onto the bobbin. I've drawn an arrow where the yarn comes out. This facilitates the twisting/winding I talked about earlier.
