Method #1 (Better privacy)

From either the Apple menu or your dock open "System Preferences. . ." then select "network".  From the drop down menu labeled "Show" select the type of connection you are using, "Built-in Ethernet" for a wired connection or "Airport" for a wireless connection; then in either case select the "TCP/IP" tab.  Your IP address will be shown in the format of "xx.xx.xx.xx".  Note that each field could contain from 1 to 3 numerical characters.  Note that this will be your local IP address whcih could be different from your "reported" IP address (see below).

Method #2 (Less privacy)

If you are using a router or a physical firewall then that device will "report" one IP address to the outside world and will assign your computer a "local" IP address.  A local IP address will usualy start with the number 10 or 192.  To find your reported address go to one of the many web pages designed to gather this information for you:

http://ipchicken.com

http://whatismyipaddress.com/