Three main ways really.
Simply putting the files and some sort of media (CD-R probably) and copying them onto the other machine is the easiest.
Alternatively you could connect the two computers up with a crossover network cable and transfer them that way. Alot faster in theory, however if you've looked at this forum much you'll have noticed all the problems that people have with networks and there setup.
Another method, is to remove the hard drive from the old computer, plug it into the new one and transfer files that way. Obviously with this method you've got to be comfortable opening up both computers.