yea rj45, aka 10baseT, a crossover cable will allow you to connect without a hub, cost me about 5 bucks for a 6 foot section about 3 years ago. You have to enable sharing for Computer A, take Computer B and double click network icon on the desktop, and you might see Comp A's name in there, dbl click on it and you should see the drives you shared. You can then map a network drive, so you can access a certian drive and dir on Comp A, from 'my computer' in Comp B using a drive letter.
So instead of "\\Computer A's Name\c\documents\user\My documents\ " it would just be G:\
Different OS's do things differently in this area so this might not go according to that plan, but thats the basic concept. Save the long version for when the short doesn't work. Then just ask questions as you get stuck, otherwise I could spend about 5 hours typing out every possible thing that could go wrong.