Fisrt off, do this:
Put eduke32.exe in here:
C:\Program Files\GOG.com\Duke Nukem 3D
If you installed to default directory.
If you installed on a 64 bit os, use this location:
C:\Program Files (x86)\GOG.com\Duke Nukem 3D
Double click eduke32.exe, and set everything up how you want it.
Play the game.
Select Save Game, click Enter
Press Enter again in a blank spot.
Type the name that you want to save it as.
Click Enter again.
Exit the game.
Double click eduke32.exe again.
Select Load Game.
Is the game still there?
If so, your settings should have been saved also.
Remember, eduke32 and the Duke Nukem 3D shortcut are not the same, and wont share user options (as far as I know) like key bindings.