Back in the Saddle

 is a starter/tutorial quest in Fallout: New Vegas.

Quick walkthrough
After character creation, Sunny Smiles offers you some training when you talk to her inside the Prospector Saloon. You then follow her outside and are required to shoot three empty bottles (Sunny will provide a varmint rifle and ammo). After doing so, you can opt to skip the rest of the tutorial or continue on with Sunny. If you continue on, you'll receive additional ammo and accompany Sunny Smiles to Goodsprings Source, where you'll clear three wells of geckos. At the final well, a woman is under attack. If you manage to save the Goodsprings settler being attacked, your standing in the community improves (upon speaking to her afterwards) and you will also receive 3 bottles of purified water. Once this final well is clear, talk to Sunny to receive 50 XP and be paid 50 caps for your help. This completes the quest, and allows the player to undertake another tutorial quest with Sunny Smiles.

Detailed walkthrough
After setting up your character via the small tutorial inside Doctor Mitchell's house, he will direct you to the Prospector Saloon, stating that a woman named Sunny Smiles will be able to help you with your dilemma. Upon exiting the house, run towards the marker and enter the saloon. When you enter, you will be greeted by Cheyenne, Sunny's dog, and Sunny herself. She tells you that the Doc informed her of your coming and to meet her out back. Follow her, and upon reaching her outside, she will give you a Varmint Rifle and 30 5.56mm rounds. A shooting tutorial ensues, teaching you about aiming down the sights and crouching. After you shoot the 3 sunset sarsaparilla bottles, she will then ask you if you would like to tag along on a little job. At this point, any time you talk to her you can choose to end the tutorial, but for the sake of 50 bottlecaps, 60 5.56mm rounds, Goodsprings reputation and 3 purified water, continue the quest.

You'll receive 60 5.56mm rounds upon agreeing to help and then run south east, towards the Goodsprings Source. Once you get close to the first well, Sunny will tell you to sneak, by crouching, to surprise the geckos. Once the geckos are dead, speak to Sunny and continue on to the next two wells. There should be two or three geckos at the next well, and two or three geckos attacking a Goodsprings settler near the final well. Kill the geckos and talk to the Goodsprings settler; she will give you 3 bottles of purified water and improves your reputation in Goodsprings. If the Goodsprings settler dies, you won't receive the reputation boost or the purified waters, but can loot her body for a cleaver, field hand outfit and a handful of caps. Talk to Sunny afterwards to receive 50 XP, get paid 50 caps and have the opportunity to start a side-tutorial about the survival skill (and lament the settler's death in dialog, if appropriate).

Congratulations! You now know the basic mechanics of combat in Fallout: New Vegas!

Bugs
It is possible for the mission not to complete even after following all of the dialogue options with Trudy at the end of the quest. After talking to her she just remains behind the bar and the mission remains active. This also seems to affect the start of another quest in Goodsprings: Ghost Town Gunfight.

It is possible for the mission to not continue automatically. if a random critter appears outside the saloon when you follow Sunny and she moves to attack she will not give you the rifle or the mission unless you push her back to where she was standing when you come out of the saloon

Sometimes all 5 or 6 Geckos are attacking the settler at the final well (before v1.1.1 - needs confirmation post patch).

Reference
The quest name is a likely reference to the 1941 Gene Autry cowboy film, "Back In The Saddle". There is also an Aerosmith song 'Back in the Saddle', released in 1977.