Connecting ethernet shield to computer
First off you need a basic understanding of TCP/IP networking. One you have that you need to:


Allocate yourself a new subnet - one that's not your normal local network (say 192.168.1.0/24)
Assign an IP in that subnet to your Arduino (say 192.168.1.1)
Assign a different IP in that subnet to your PC (say 192.168.1.2)
Configure your Arduino's sketch with it's IP address and netmask
Configure the PC's Ethernet interface with it's IP address and netmask
Connect the two together with a suitable cable.  If the PC's Ethernet port doesn't have auto-direction sensing you will require a special cross-over cable where TX+/TX- and RX+/RX- are swapped over.