Thieve Faction Mission: Loose Lips
If you look on the map you should have no trouble finding the Thieves HQ towards the center of the map in the middle -- in between the two entrances for the HQ is a marker for Assignments -- head to that now and talk to the Thieves Guild Officer to learn that there is trouble in the air -- someone is paying the Guards to apply pressure on the Guild.
Proceed to the checkpoint and hire the Thieves to distract the guards and steal the bribe -- when the guards move away one of the thieves will rob the chest while you head down by it and use Eagle Vision to scan the crowd there to ID the agent. Once you ID him follow him discretely as he leads you to the person who has been funding the scheme.
Loose Lips -- The Thieves Guild Faction Mission
Climb the wall gaining access to the walkway above the courtyard where the two are meeting to trigger the next CS, after which you should hire the Thieves here and have them distract the guards in order to lure the man out of the courtyard. It is important that you do NOT kill him inside the red protected zone that covers that courtyard -- there are plenty of buildings adjacent to the courtyard that you can use to watch him leave and, once he departs the security zone, kill him.
After you kill him you may have to deal with a few guards, then you need to loot him to complete this part of the mission. After you loot him you will trigger the final CS in which you talk to the Thieves Guild Officer again, and learn what happened on his end of the mission. After the conversation ends you get the notice that you gained 100% Synchronization -- good on ya mate!
Completing this primary faction mission now gives you access to the rest of the missions, which we will now be doing as in addition to adding to the Synchronization they will also give you the Thieve-looting ability, which is required for one of the Achievements.