To play a map: Select the map to be played in the list and click the Play button. Duke Nukem will launch with the files and settings needed for the selected map. When you quit the game Duke Nukem will be restored back to it's previous state.
Difficulty settings for maps that support them are set to Let's Rock by default. You can change this default in the Preferences window and it will apply to all maps added from then on. You can change individual map difficulty settings in the View Details window for a map.
If a map fails to load using this method, please see When It Doesn't Work for possible solutions.