Monitors tend to be fairly standard. xfree (the Linux windows server, i.e. the thing that runs your GUI) has generic monitor drivers and whatnot. Search Google for the specific make and model of your computer, like "Toshiba laptop 4001blahwahtever xfree monitor driver" if you want. You're more likely to have problems with a generic video card than with a generic monitor.

As for what you would need to carry it out, you'd need to pick a distro, get the CDs for it, and follow its install instructions.