Network is set up, but my Mac won't recognize it!

Do you have an airport signal showing in the top right of your screen?
If so, try connecting to the Linksys - open a browser window and enter the address of the router, something like 192.168.1.1 probably, but check your Linksys manual. If you can do this then you know the wireless network is ok.
By the way, whatever your Linksys ip address is, make sure your computer ip address has the same first 3 sets of numbers. ie If the linksys is 192.168.1.1, then the computer should be 192.168.1.x, where x can be anything from 2 to 255. If you have set DHCP to automatic then the router will automatically allocate a working ip address.
In addition, make sure that your location is set to 'automatic', and that you have turned off your firewall - this makes setting up a bit less prone to problems, and you can mess about with these things later if you want to.