Out of the Abyss' chapter 2 will likely be the most looked up 'cause it describes Underdark's environment and how to move from one place to another.
Just after the escape from the stronghold, PCs will have to decide where to go to reach the world above.
You'll use and look up this chapter every time PCs will move to another place.
Have a copy of this chapter for an easier reference during the game session.
There you'll find:
- Distances (in days of travel) between different places and a map
- Random encounter tables (creatures and places)
- Description of effects and special areas (magical and not) and of creatures and plants
- How to handle the Drow's pursuit of the PCs (what would you have expected? had you really thought Drow would have given up so easily?)
- Some useful side quests
It's obvious most of this stuff can be easily used in other adventures and campaigns than OotA, so you can think about this chapter as an Underdark's mini-sourcebook
Random encounter tables (at least about creatures) have little variety. You must seriously think to expand them.
The real difficulties of this chapter, which you'll have to deal a lot of times, are about the travel itself.
Do PCs know where to go or do they need a guide?
Do they see in the darkness or do they need light (magical or not)? Better slower in the darkness with the danger of being caught by the Drow or faster with light but with the danger to attract more dangerous creatures?
Can they forage regularly?
Do they have a satisfactory equipment?
Calibrate carefully those difficulties according to your susceptibility and your players'. To give full effect to them means to settle the game at an hard level. Some players will simply not accept it, being frustrated.
After a trip, harder or easier, PCs will arrive somewhere. You'll see those places in the following posts.