So presuming you're using windows.
You run the GOG installer
You click this link: http://dukeworld.duke4.net/eduke32/synthesis/eduke32_latest.zip
You unzip the download into the folder where the GOG installer put the original game. (Something like C:\Program Files\Gog.com\Duke Nukem 3D, but that might depend on your computer and my fuzzy memory.)
You double click on the resulting eduke32.exe
If you want you make a shortcut to eduke32.exe