Residing in a series of temples throughout the Valley of Death, they are the rivals of the Gerudo. Their elders reside in the highest parts of the the temples and are rarely seen on a normal basis. They have countless books and literature on the history of Hyrule and are the most knowledgeable about the world, magic, and combat. The elders are the only ones in all of Hyrule other than Ganondorf who are familiar with the ancient Hylian Language, far different from the modern dialect.
Shiekah are met first, and initially present themselves as pompous and arrogant. He meets with the elders, however they obviously won't let Link anywhere near the cog since they know to protect it. They also think that there is no danger in Hyrule, since the Gerudo are still kept out.
As Link approaches the desert, The Hero's Ghost confronts and fights him. Link is defeated, but escapes into the desert when he throws a dud Deku Nut to the ground. As the Hero rushes to finish Link, the Deku Nut goes off and Link falls backwards into a sewage pipe leading into the Desert. The Hero elects to not finish him.
In the desert, Link is captured by the Gerudo. The Gerudo initially seem beat-down by the Shiekah, and Link sympathizes. He meets with Abigail after escaping and sneaking into her quarters and they work out a deal. He'll help them because he likes helping people, and because helping them attack the shiekah will allow him to get close to the cog.
Link is to prove his worth by going to one of the major Shiekah outposts, long abandoned. Fighting his way through traps and creatures, he finds the Fire and Ice Arrows, left there by the Shiekah. He brings them back and turns them over to the Gerudo. Abigail explains to Link that the Fire and Ice arrows were designed by the Shiekah and are used as a key on many locks in their fortress. They begin preparing to storm the fortress.
Link is given the task of gathering some weapons from the storehouses. Inside one of the houses is a treasure chest belonging to a high ranking Gerudo. It contains a note. The note is from Abigail herself and it detailed the attack against the Shiekah. It also contained the horrible things that the Gerudo were planning to do with the Shiekah once they were defeated.
With his mind now torn and conflicted, he decides to go to the Shiekah Fortress just to see what was going on. Just before he leaves, he is attacked by the Gerudo he stole from.
Link defeats her in battle and quickly goes to the Shiekah Fortress, which he finds under attack by the Gerudo. Fighting his way through both Gerudo and Shiekah, he sees Abigail heading for Seere. He chases her through the fortress eventually to a path leading to the temple. Using Fire and Ice arrows, Abigail and Link are able to unlock a number of doors leading through parts of the fortress that haven't been opened for years, some parts crawling with Redead.
If you helped more Gerudo, then the elder will call upon his body guards, and Abigail will say, ha, it seems they've busy losing the battle. Or in the other case, the elder will say, oh so you came alone? Or did all your reinforcements lose to my warriors? Either way, they'll start to fight, and Abigail will shoot a fire arrow Link's way, burning down the path to get to them to interfere.
Only one path remains for Link, which is in the direction of the Temple entrance. When he gets there, he is confronted by Seere. He talks to Link, saying that he's seen him in visions. He might bring great destruction, or salvation- only the path of shadow will show the truth: and he opens the gate to the shadow temple, and pushes Link in- initiating the first battle with the boss, which Link can't destroy, but can fend him off.
Then when Link beats the boss and comes back out of the temple, Seere is standing at the temple's entrance, looking down on the battlefield. Whoever's side you helped more, that leader (Abigail or the elder) has just defeated the other in battle. Their second-in-command is talking to them. Seere explains the situation to Link:
[Whichever] has been defeated, but both sides suffered so much loss that the Shiekah can't hold the desert pass, but the Gerudo can't advance anymore and are retreating. The Shiekah city/fortress is in ruins. Seere says something like "I don't blame you for this, you just added a spark into years and years of kindling. In fact, I'm still not sure whether you're destroying Hyrule or bringing about the healing we've been needing for ages. But that's just me- these guys, they definitely think you're to blame." And several Shiekah warriors jump into the scene. Link has to escape the ruined Shiekah fortress to lose them.