One for My Baby

 is a quest in Fallout: New Vegas.

Quick walkthrough
Talk to Boone. He will mention his wife during conversation. Offer to help. Ask No-Bark Noonan about Boone's wife. He will mention the Dino Dee-lite Front Desk. Sneak in at night and obtain the Bill of Sale from the safe behind the desk. Ask Jeannie May Crawford to see what is in front of the Dinosaur. Put on your beret and lead her there. Go back to Boone. After you complete the quest you can ask him to join you and he becomes your companion.

Video walkthrough
For a video on how to do the quest, you can go here:

Detailed walkthrough
1. Go to Novac between 9 PM and 9 AM. Find the giant dinosaur and enter it. Once inside, head up the stairs and go through the door at the top. You should meet a man named Boone. Talk to him about his wife and you will receive the quest to find out who sold his wife off to slavers so he may kill them. He also gives you his beret to wear as a signal to fire on the person you bring in front of the Dino.

2. You are then given the task to talk to select inhabitants of Novac. Luckily, you only need to talk to one of them in order to progress in the quest. This person is No-Bark Noonan, an older man that seems a little out of his mind. You can find his shack behind the motel. Talk to No-bark about Boone's wife and he will tell you about strange business in the motel lobby. (If you have a high enough speech level you can finish the quest without evidence. Just talk to Boone after talking to No-Bark Noonan)

3. Head to the front desk of the motel and once inside check behind the counter to find a safe in the floor. This safe is locked and will require you to either lock pick it (easy skill) or pickpocket the key from Jeannie (there is no loss of karma). Inside the safe you will find a note titled Bill of Sale. This document tells of how Jeannie May Crawford sold Boone's wife off to slavers.

4. Now you have the evidence so confront Jeannie at night and ask her to take a stroll with you in front of the dinosaur. Once in front of the dinosaur put on the beret and Boone will kill Jeannie and your job is done.

5. Head up to Boone. He will ask you how you knew it was her (this is where getting the evidence comes into play) and you tell him about the bill of sale you found. If you did not get the evidence you can use speech on him but if that fails he will try to kill you. If you told him about the evidence you can keep talking to him and make him become your companion.

Bugs

 * If you cannot get Jeannie to follow you, try the following solutions:
 * Use the Wait function to move the in-game time between 9PM and 9AM. Suggest moving it to a comfortable time between then.
 * Change your tracked quest and fast-travel out of the town. Return, retrack the quest, and attempt to confront Jeannie
 * Try speaking to Jeannie at her house at night, not while she's on the street or in the Motel Lobby.


 * Obtaining the evidence before speaking to any NPCs in Novec will result in a quest completion for the optional objectives.


 * Obtaining the evidence before talking to No-Bark will result in a quest completion for the optional objectives.


 * If you talk to No-Bark Noonan and before meeting for the first time Boone he will confront you as if you already know him, skipping dialogue and interaction with the character that would have been available before you accepted the quest.


 * Having a higher than typical amount of reputation in Novac can result in the quest not beginning.


 * Binding Boone's Beret to a Directional Pad key may result in a console crash.


 * After completion of the quest, if you have Boone join you as a companion he is supposed to gain a set of armor, this may not happen. This bug may also occur on PC.

--Confirmed, Boone takes back his beret and gives you a different beret. The original having no bonus critical. However, after joining you, he has a second similar beret, also with the critical hit bonus.
 * After the quest is complete, Boone clearly takes back his NCR beret, but the player can still find it in their inventory. --Needs Confirmation, Boone gives you a 1st Recon Beret as a reward for the quest, and takes back his.  Are you sure that's not what your seeing?