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Search and Rescue - Introduction
This is an incredibly quick mission that you can get from the Underground Railroad board down at the Kirkwall Docks. Speak to Mistress Selby after you receive the relevant letter to open up the quest book behind her. You can then accept this quest to open it up on the Wounded Coast.
Note that there doesn't seem to be any impact on relationships for this mission. It's a pure side quest for money.
I suggest that you bring a healer, a tank and then two damage dealers (rogue or mages, depending on preference).
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Search and Rescue - The Cave
In all honesty, finding the cave is probably as difficult as actually freeing the mage.
You need to go to the Wounded Coast, and then walk all the way back to the cave that the Qunari Tal-Vashoth used in Blackpowder Promise. It's to the far back and up the side path. As a side note, if you've got the Herbalist's Tasks quest for this act, the flower that you need will be growing just outside the cave's entrance. Grab it on your way into the cave.
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Search and Rescue - Saving the Mage
Rescuing the mage isn't that hard, at least in concept. You need to first enter the cave, and engage the door guards. This is a very weak group that will barely be a speed bump for any decent party. You should be able to just tear right through them and keep moving on in a line toward the big cavern in the center.
This is where the real battle will be, and it is certainly a battle.
There are a bunch of basic mercenaries, along with two assassins and a mercenary commander. They are broken up into waves, but if you don't handle this well it's easy to lose. The first step I found was to charge up the steps and attack the commander. Killing his men just causes more to spawn, so focus on taking out the commander first. If you can, look for the assassin and pin him down too. Remember that simple combos, such as freezing a target and then hitting him with an ability, like Mighty Blow, can cause a ton of damage.
If you take out the assassin in the first wave, then the fight's manageable. A tank can tie up the mercenary while a fight bottlenecks the grunts at the stairs and protects the ranged fighters. The second assassin can be a bit of a monkey wrench, but hopefully you'll still have enough stamina to take them out quickly too with a few well placed blows and spells.
Once the mercenaries are dead, you can talk to the mage at the top of the steps to free her. This will officially complete your goals. Just backtrack out and back to the Kirkwall Docks. Talk to Mistress Selby to get bonus XP and your sovereign reward.