What's the problem you're having?
I've always had good luck in assigning each computer a static IP, usually 192.168.0.2 and 192.168.0.3, leaving the router to receive the dynamic IP assigned by the modem.
A good diagnostic methodologyy I've used:
1. ping the router. Did you get a return? If yes, go onto step 2. If no, check the network settings on the computer. Where's it getting it's IP from? Gateway info? DNS info?
2. Ping
www.google.com (they let you ping them, some places simply drop a ping packet). Did you get a return? If yes, it should be good. If not, check your DNS settings.
3. Ping the other computer (you need to know it's IP address, this is why I like static IPs). Did you get a return? Yes, no problem. No, make sure the receive is accepting pings, check the firewall software/settings.