Dungeons is a map in the Castle of Grief. It is the 24th map in Hexen, and is named MAP25 in HEXEN.WAD. You will only need to make one visit.
You will arrive in a small room with a portal back to the Gibbet. There is a staircase leading down to the main room, which has a central lava pool full of Afrits. At the far end is a barred passage, and to the right/west there is an open stairway. Watch out for an Afrit next to the stairs. You will enter a dark dungeon area shaped like a rectangle, full of Afrits and Ettins. At the far end of the rectangle is a skullface switch. This will open the barred passage, which leads into a large ring area. From the center you will see seven prison cells which you can't enter just yet. Around the perimeter, there are Ettins, as well as Flechettes and Discs of Repulsion. Going back out of the passage, you will see a sun/moon switch facing you on the pillar. You can press it 7 times - each time opens the back wall of a prison cell and generates a Slaughtaur. After they're all opened, another sun/moon switch will appear on the pillar in the center of the southern ring area. This will open two new paths in the main area by the western dungeon entrance. You can ascend either one to get to the balcony of the dungeon area. One has Flechettes, the other Crystal Vials.
To find the exit, first go back to the first cavernous room with cells. The first cell on your right will contain a bullhead switch. This will open a wall in the passage leading in from the dungeon. You will enter an area with a Centaur and a sludge river with Stalkers. The river enters a cramped, shadowy area, which ends in a bottomless pit. But don't panic! This particular fall will transport you safely to Effluvium.