Can I hook up two computers and play games without using the internet?

For starters keep in mind that I'm not a tech savvy individual. I have dial-up. Enough said. I'm getting a second computer in a sweet deal and I want to know if I can hook it up to my origional computer and play games with another person without using the internet. Because dial up stinks. I've heard something or other about a "crossover cable." Thanks for your help.
-Darman