The way to avoid the computer to computer stuff is to set the wireless router for "infrastructure" mode. This makes IT run the wireless network. It should be in this mode by default. When your computer detects the wireless network, it should offer to join that network, and when you join the appropriate settings are automatic so you should be in infrastructure mode (and NOT computer-to-computer or "Ad Hoc").
Now on to the OS X computer. It too should detect the wireless network, offer to join it, and make all the right settings for proper connections. NOW, you have to go into System Preferences and enable the correct level of sharing-that's up to you. I'll bet you are only lacking the sharing options right now.
Cheers!