The easiest way would be to install a cd-rw drive into the old machine and copy the files onto a CD. Then put them onto the new machine. If there is a CD-RW drive in the new machine it would be easy to swap it around if you are confident with opening the machines.
If you have a network card on both machines, you can get a network crossover cable and do it that way - slightly more involved but also a viable proposition.
What OS is on the old machine? If you want to sell it, the best thing to do is use a factory restore disk if you have one. Otherwise format the hdd and install the OS onto it. How you go about this will depend on the current OS.
If you are worried about the security of the data on it at the moment, it might be worthwhile getting a program like eraser which goes a long way towards deleting the files so that they will not be easily recovered.