Ok, after you hear about the Redguard woman, go to the Bannered Mare and speak to Saadia , the Redguard. She wants to speak to you in private. From here you can either FOLLOW HER or go find and tell the Alik'r warriors where she is.
Note: If you want to just go tell the Alik'r where she is, follow the guide in the box. If you want to listen to her, skip the box.
When she tells you to follow her, LEAVE the inn. Look at your map and find the marker on the map that shows where the Alik'r warriors are at. They travel around, but you can often find them in some inn or other. Once you find them, fast travel there and go tell the warrior where Saadia is at.
They will tell you that you will have to lead her out of the city, to Whiterun Stables , where they will be waiting. You can now return to the Bannered Mare and speak to Saadia and tell her a series of lies to get her to follow you. She will run to the stables, so stay behind her to make sure she goes through all the doors ok.
Once you are at the stables she will realize your treachery and will have a brief chat with Kematu . Kematu will paralyze her next, and after that you can talk to him to end the quest and gain a 500 gold reward, as well as learn what exactly she did.
She wants to speak to you in private, so follow her to her room. Once in here, she takes out a dagger and wants to attack you . Tell her to relax and agree to help her. Time to go find the Alik'rs.
Go to Dragonsreach and instead of going in; go to the back and enter the dungeons . In here, simply walk to the prisoner and speak to him. He offers the info if you pay his fine. Pay any guard 100 gold and let the prisoner know his fine is paid. He tells you where Kematu is, so leave the dungeons, leave Whiterun completely and time to go to Swindler's Den . Make your way there and go inside... duh!
In the first room, you'll find two bandits and two more in the next room. Easy enough. In the third room though, there are around five of them, plus a magic user on the upper level. Take care of the magic user first if you can. After that, follow the path until you meet with Kematu. He asks you to lower your weapons. From here, you can either continue and kill him, or have Saadia be taken to justice. Either way, you'll end up with 500 gold and the quest will be at an end.
Note that this all depends on you. There's no way to tell who's telling the truth, so just follow your gut.