No, ideally you won't have the same IP.
By OS I meant operating system, sorry about the acronyms... Basically what version of Windows? XP? Vista? Seven?
EDIT:
All the kids have Vista/Seven these days I guess so I'll give ya that one...
1> Go into your control panel and open the Network and Sharing Centre.
2> Find the network you'll be using below the network map (there is probably only the one, if not, pull out the ethernet cable on one end and see which one you lose that's the one you want), it will probably be called something like 'Network 1' and say 'Local Area Connection'.
3> Click 'View Status', to the right of 'Local Area Connection'
4> In the dialog that opens, click the 'Details' button
5> Your IP will be four 1-3 digit numbers seperated by dots in the 'IPv4 IP Address' field, for example 192.168.1.1
You'll only need to know one person's IP - this person will be hosting the game, and once it is set up, the other player will go thru 'Direct Join' and enter the IP when prompted.
Hopefully works for ya.