Well first you make a backup copy of your original .exe, which should be by default in your
C:\Program Files\The Ur-Quan Masters\ directory.
The file mentioned is named
uqm.exe, you can change the
name to something else like
uqm-original.exe. Don't worry if you can't see the
.exe bit in the filename. By default that view is turned off.
After you have completed the above you can UnZIP the mod you downloaded straight into the directory aformentionted,
which again by default is
C:\Program Files\The Ur-Quan Masters\
When that is all done you can run the game.