boot up in safe mode.. this increases system stability by disabling most common driverss that may lead to a crash during your investigation of the problem
goto 'event viewer' --> 'Windows logs' --> 'System'. (Feel free to check out the rest of the stuff in here later on as it's good to read through.)
the list in there contains logs most noteable events in Windows - hence the name. Even though you're machine is randomly rebooting right now, odds are the problem was being logged long before that. Windows may even have popped up a dialog window at some point along the way and told you as much.
By clicking on the 'Level' tab at the top of the list you can view these logs in level of severity rather than the traditional chronological view. You can Google error codes in these logs if you don't know what they mean.
A failing AMD/ATi video card log usually list as AT***.* as the source.
A failing NVidia video card log usually list as NV***.* as the source.
*Critical* errors are the ones we're most interested in here.. there's a whole bunch of them, and they're all categories and numbered so that they can be looked up later online if need be. Here's one I had back in August
after a game clashed with another background program and went on to lock up on my PC.
Keep in mind that it's not uncommon to see videocard errors in the logs under the 'Warning' level. This is usually driver/program glitches. For example, if I use FF to view more than 2 YouTube tabs my video will fail and then recover - resulting in a yellow 'Warning' error being logged. I still don't know for certain whether this is a hardware driver issue, card firmware fault, FireFox bug, or whether the computer just couldn't handle that much donkey pr0ns :/
Hope this helps.