Yes, you need a "wireless" router. If his laptop already has built in wireless support, you're all set once the wireless router is connected. Internet is instant, unless your network is secured (in which case, he needs the password to get in).
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Cox I assume is cable. Setup the wireless router in your room where the cable modem sits. Connect the Wan cable from the cable modem to the Internet port on the back of the wireless router (or something like that). But you have to have them connected together regardless. That's it. If your roommates has build in wireless laptop, he will be able to get in in a snap.
If you're running wireless too, then you're set to go. If you don't have wireless support for your PC, just connect the ethernet cable from the back of your PC to the back of that wireless router. Instant connection.