Crossover network cable (a regular netowrk cable may work as well) and compatible IP addresses...
IP Addresses: 192.168.0.2 & 192.168.0.3
Subnet Mask 255.255.255.0
Default Gateway (even though it does not exist): 192.168.0.1
The above should work if your PC is not connected to a router. Depending on the router and the address range that it uses, you may have to change from 192.168.0.x to 192.168.1.x (or similar).
If you need to have the Xbox360 connected to the internet via the PC, it is possible to route traffic through the PC, but you will be much better off with a router/firewall
1: Dimension 9200 - Vista Ult, 2.4GHz Q6600 Core2Quad, 4GB RAM, 160GB, 750GB, 500GB USB, Nvidia 8300GS, PVR-150, HDTV Wonder, Vbox 3560, X360, DMA2100
2: HP m376n - MCE 2005, 2.6 P4 w/HT, 1GB RAM, 250GB, 400GB USB HD, Nvidia 6200, Emuzed MAUI, X360