I was wondering how I would go about wiring a small fan (like a computer fan) into my tube amp to keep it cool. Would I just wire it to the power cable? Or is that the completely wrong thing to do.

you'd probably find some kind of half-acceptable voltage around the heater power supply. Might work.

otherwise find a 12V DC wallwart and shoehorn it into your amp somewhere
get one of those powered usb hubs that can run off an ac adaptor then a hook up usb powered fan. it's probably the easiest way to do this without messing with your amps wiring.