The underground
The stairway entry to the Dungeons(or underground, as the manual calls it) is at the bottom right screen of the Forest, the farthest screen from the Village. It has 3 levels, 10m, 20m and 30 meters. Many rooms are dark, and you may light them with a Wand of Lighting, or a Blazing Cape.
Many tiles in rooms & corridors (except doorways) are rigged. You may also find blue portals to Slaeter's Sea.
Monster difficulty and trap frequency increase as you go deeper. Each dungeon level is nominally made of 3 x 3 screens, but level 10 and 20 don't have a passageway to the upper right screen. You can make a passage to the next screen with a wand of tunneling, at any time. Level 30 does have links to the upper right screen, and stairways to 20' and 10'. It is likely that you will find the toughest monsters in the upper right screen, including Scyld. You will also find red portals to Mimer's Realm on the hidden screen on level 10m. The left 3 screens on Level 30' are the Crypt. It's accessed from a hidden stairway on level 20', or by tunneling. The bottom center screen is Vidur's Temple, and can be reached by tunneling on level 30', or from a hole on level 20'. The lower right screen of level 30' is the Bazaar. There is no way to tunnel into this area.