Picking Up the Trail

 is a Fallout 3 quest. It is also a Xbox 360/PC achievement and a PlayStation 3 Trophy.

Gain entrance to Vault 87.

Scribe Rothchild
Scribe Rothchild can usually be found in the lab of the Citadel. If you are in a hurry you can just access the Vault-Tec Terminal (Vault 87 section) in the A Ring without consulting Rothchild. If you ask him, all he will tell you is the location of the Vault-Tec Terminal.

Once you've consulted the terminal, Rothchild will show you its location on the lab map panel. He also warns you about high levels of radiation around the vault's main entrance, which leads him to hint at the location of Lamplight Caverns.

Lamplight Caverns
Mayor MacCready will stop you at the gates of Little Lamplight. You can convince the mayor to let you in with a Speech check or by talking about butts with him if you have the Child At Heart perk. Otherwise the only way through Little Lamplight is to help rescue Sammy, Squirrel and Penny from Paradise Falls by doing the side-quest Rescue from Paradise, which is an Xbox 360, PC achievement, and Playstation 3 Trophy.

Once you get in Little Lamplight, there are two ways to enter Vault 87:

1. Survive Murder Pass. You must speak with Mayor MacCready or Princess to get the gate to Murder Pass open.

2. Learn from Mayor MacCready that there is a door that won't open. This is a back door to Vault 87. You must ask Joseph to restore power to the computer terminal before you can use it. The door and terminal (average difficulty) are located in The Great Chamber.

Bugs
If Princess is located near Murder Pass when you convince MacCready to open the gate, there is a chance that she will become stuck in the closed gate, preventing MacCready from opening it. If this happens, the only way to continue is to take the alternate route through Joseph.

It's possible that this quest will be considered "completed" and move you onto the next quest before you get into Vault 87. In my case it happened when I entered Vault 92, before I'd even discovered Little Lamplight.