It depends on whether you're trying to play Fallout 1, Fallout 2 or Fallout tactics.
Anyway, for fallout 1, Download the official and unofficial patches first. Download and install the latest High-resolution patch afterwards. Set it to the appropriate resolution in-game. If that doesn't solve the issue, Change it to 16-bit (or 32-bit if it was already on 16-bit). That should solve it.
For Fallout 2, just find the final unofficial FO2 mod and patch it. It should work once you set the correct resolution in-game and restart.
The patches are really, really easy to find. Just type down fallout unofficial patch or something into Google. I hope that helps. Have fun, they're both excellent games.