A really old way (but effective) is to use a direct cable link through serial ports, as most computers have these. By today's standards, the transfer of files would be slow.
If both machines have a network capability, use a CROSSOVER cable and connect to each machines network card. This provides transfer rates at the lowest of the two cards capabilities, but is unlikely to be less than 100Mbs (theoretical).
The third option, is to go the whole hog and use a router, where you connect each machine to the router. This, whilst being more expensive initially, provides an upgrade path in as much as, it provides the capability for each machine to connect to the Internet simultaneously.