High Times

High Times is a side quest in Fallout: New Vegas.

Detailed walkthrough
Speak to Julie Farkas. She is a doctor with the Followers of the Apocalypse at The Old Mormon Fort. During dialogue with the Courier, Julie mentions two men who are addicted and asks the player to find Bill Ronte and Jacob Hoff and help them. Agreeing will begin the quest.

Bill Ronte is located in Freeside, in an abandoned house located across the street from the Silver Rush. He will tell you about how only Dixon's alcohol will calm his addiction, and that the withdrawal symptoms are too strong to quit.

Jacob Hoff is found in the crumbled building across from Mick & Ralph's. He is sitting on the ground directly forward as you enter the building. He will say he feels young and strong when he takes Dixon's chems, and that it's too hard to quit.

After speaking to at least one of the addicts, speak with Dixon (the source of the addicts' problems). He is found outside of Mick and Ralph's store, near where Jacob is found. After a Speech check of 35, Dixon will agree to leave the addicts alone. The Courier can also bribe Dixon with 300 caps or kill him. A Speech option to attack him makes him aggressive, so killing him will not affect your Karma. With the Black Widow perk, you can also convince him to leave Bill and Jacob alone. Then you can approach the men and help them deal with their problem.

Jacob will ask for 10 doses of Fixer to help him clean up, but passing a Science check of 50 allows a combination of Fixer, Psycho, and Buffout instead, or pass a Speech check of 50 and Jacob will clean up on his own.

Bill can be convinced to head to the Fort with a Speech check of 50. However, if you tell him "You won't be seeing Dixon anymore.", a dialogue option involving detoxing with 2 doses of Fixer, Whiskey, and RadAway will appear where you can pass a Science 50 check to skip the RadAway. The Speech 50 check to go to the Fort can then be used to gain experience from both skill checks.

If you can't pass the Science and Speech checks, Fixer can sometimes be purchased from Dixon or from the bartender in Brimstone, the bar/strip club located in Gomorrah.

Also take note that several Freeside thugs may spawn after sending each addict to the Mormon Fort; letting the addicts die may negatively impact the rewards of the quest.

After speaking with both men, return to Julie Farkas at The Old Mormon Fort. She will thank you for helping the men and offer you a discount on her services. You will also be able to get one free stimpak, Fixer, or RadAway every 24 game hours from Julie. This will finish the quest.

Behind the scenes
When a person takes drugs to get to a satisfying point, it gives them a "high." That is most likely why the quest is called High Times.
 * There's also a magazine titled High Times.