It's been brought to my attention that we don't have a guide for Down Below yet! So here is a very rough one that is definitely missing things. Please add, edit, and organise as needed.

First up: you unlock the relevant quest through a Distraction from The Watcher with the subject line “I need a favour.” You may first need to check out the “Intriguing-looking hole in the ground” in any Outpost, may first need to reach level 10, and may first need to complete some early quests.

Now for miscellaneous facts and advice, which will make more sense if you've unlocked the area in-game:

If you have any questions beyond this, please go ahead and ask them in Banter - or if that doesn't net you an answer, tack them on the end here and you might get lucky. Good luck down there!

1)
Back when Down Below was new Contestants used to tip each other off about the current Outpost levels by posting them in story chat / scratching them into the walls as a marker for others. Unfortunately the floors change quickly enough that it's only kind of useful.
2)
I thought it was a few thousand, but have since been informed it's maybe as much as 14,875 cigarettes for a full Clan Buff. Make your choices accordingly.