Doc Mitchell can be lied to, then he must be convinced with a Medicine skill check of 25 to provide aid for a "hurt traveler down by the highway".
If lacking in the appropriate skills, the player can always buy the supplies, pickpocket the doctor, or simply kill the doctor and take the supplies.
Head over to Joe Cobb and give him the supplies, and help the Powder Gangers invade Goodsprings. Most non-player characters in town will become hostile, but the player will receive assistance from several Powder Gangers.
Once the residents of Goodsprings are dead, the player can talk to Joe and claim the reward.
Which ever quest the player chooses to complete will affect reputation with both factions and simultaneously cause the player to fail the opposing quest, so be certain who you want to help beforehand.
If Joe dies during the course of the attack on Goodsprings, but if the attack is successful then the quest will end once all hostile Goodsprings inhabitants have been killed and grant the XP reward to the player. No further reward is obtainable since Joe actually dies (instead of just being 'unconscious') and cannot be spoken to. (Verified on PS3 and Xbox 360)
If you have already spoken to Ringo and agreed to help him, Joe Cobb will dismiss you when try and ask to help him take over the town. Each time you ask he'll claim he doesn't like the look of you.
Once this quest is completed, surviving Goodsprings citizens will sometimes say "That was a hell of a way to repay Doc, if you ask me." when interacted with.
Chet does not take part in the fight, and still runs the general store after the quest is completed.
Two small dialogue options were cut from the quest, pointing to an additional task Joe would have asked you to perform: freeing the town's bighorners. While Joe's responses are not present, presumably this would have been intended to create chaos in town. The option was likely removed owing to the presence of free-roaming bighorners in Goodsprings in the final release of the game.
xbox360ps3pc When you kill Ringo and inform Joe Cobb, he will ask you to get supplies from Chet and Doc Mitchell. Before you get supplies you can kill Joe and fail the quest, but Chet and Doc Mitchell will still be locked in the 'Help the Powder Gangers' dialog speech, and you can get infinite experience, leather armor about 1/2 repaired, 30 9mm rounds, and Powder Ganger fame. (See Fallout: New Vegas exploits.) [verified]
pc Sometimes, the mission will mess up. Even through killing EVERY citizen in Goodsprings, Joe Cobb will still say that there are people to kill. When attempting to talk to Chet, he will simply say, "Can't talk now, there's a gunfight!". The mission is stuck in this limbo forever. Starting a new character will not resolve this issue. (This issue can happen cause Doc Mitchell stuck in his house. You will have to go there and kill him yourself to complete the quest). [verified]
pc Occasionally you will not be able to loot Doc Mitchell's body if you kill him. Saving and reloading does not fix this bug. [verified]