Baseline (Widescreen) Solution & Issues
Just go to the video options screen and select your resolution there. A couple of things, though, you will need to scroll through a LOT of resolutions to get to the widescreen ones (don't select a resolution described as "tall pixels" even if it looks like widescreen). Also, the list includes every resolution the game can support, even if your system can not support it; if you select a resolution and the game switches to 640x480 mode, it's because your system doesn't support that resolution. Also, do not touch any of the other video settings that look important to widescreen (like canvas size and FOV); the important ones will get adjusted automatically.
Ultra-Widescreen (21:9) Specific Solution & Issues
Eyefinity / Surround Specific Solution & Issues
You need to edit the file "config.cfg", preferably with textpad. If you don't have any expansion packs, you will find this file in the folder "Id1." If you do have expansion packs, you'll also find it in the folders "HIPNOTIC" and "ROGUE," and you'll need to edit all three of them to make TH work in all three games.
In config.cfg, find these lines:
Edit them to set your resolution. Be careful not to mix up height and width.
In addition, find this line:
If it's not there, add it in. Set it to one third of your vertical resolution, rounding to the nearest integer. For instance, if you run 3840x1024, this would be 341. You're doing this so that the HUD doesn't stretch.
4k UHD Specific Solution & Issues
Stereoscopic-3D Solution & Issues