Intimidate Garl for her release (45% Speech required).
Quietly kill the two guards at the rear of the building and pick the lock on Tandi's cell.
With a Luck of 9 (and male gender, and you are wearing a leather armor or using a Stealth Boy), the raiders will mistake the Vault Dweller for Garl's father whom he killed to take control of the Khans (50% chance). With at least 6 Intelligence and a Charisma or Speech check, the Vault Dweller can bluff Garl with this ruse and secure Tandi's release.
The first and second methods of rescue entail a lot of risk, the second method especially if the Vault Dweller is still a low level, as Garl is a highly competent brawler and much more experienced than his men.
Tandi can be used as a party member if the Vault Dweller never takes her back to Shady Sands. However, since you cannot give commands to her and she lacks combat skill she is undoubtedly the weakest of all possible companions. Still, she deals a decent amount of damage against raiders.
Asking Seth for money will make him behave aggressively, but not make him hostile. Though, should the Vault Dweller say they won't do the job without hearing about the reward, Seth will flip and then turn hostile (along with nearby guards and Katrina). While it is possible to escape to the worldmap, this effectively locks the player character out of Shady Sands, as Seth remains hostile.
Killing the Khans before Tandi is kidnapped will obviously rule out this quest. Likewise, if the quest Join the Khans is completed, the same will happen.
When escaping from the base with Tandi, a note will appear: "You gain 0 experience points for freeing Tandi." (Only for the violent solution. For freeing her non-violently, you will receive 400 XP.)
If the Vault Dweller has Ian as a companion, and fights Garl, he may get into the ring. If this happens, he will attack Garl; (Unarmed or by shooting as well) when Garl does not. This helps to end the quest significantly well. If Ian is outside the ring, he cannot help. [verified]