I originally had two Windows XP laptops and had one wired and used the other wirelessly. The way it was set up was so that one would be connected to the internet through my cable modem, then I would set up an ad-hoc (MANET?) connection, and use Windows ICS.

I haven't changed anything on the computer that is still connected to the internet, but I've installed Ubuntu on the laptop I want to use wirelessly, but it can't connect to the ad-hoc network. I've tried using DHCP and using a manual configuration, but I don't really know what else to do...

Can you not connect to the Ad-Hoc network, or can you not establish TCP/IP with the other machine? Those are two very different things.

The first thing would be to verify your WiFi card is supported and working correctly, and if it is, see what the problem seems to be with connecting to the other machine. Some drivers do not support Ad-Hoc mode, so it is possible the card simply can't do it under Linux, in the worst case scenario.

If you can detect and connect to the other machine, then you will likely need to setup a static IP just as it was configured under Windows. Make sure DNS is setup properly, and that the other machine is setup as the default route.