When you're ready to go, just pop out to the city map and go to his estate. You should meet your contact there. I believe you need to go to the right. The path on the left is the long way around and I ended up in a fight with a few guards. Regardless, you can kill a few guards out here and it doesn't seem to affect anything.
Once you make it to the marked service entrance, just talk to Erlina again to put on the uniforms. Note that you can fight if you really want to do it. I'll assume that we'll use discretion though. Walk through the palace and follow the fairly simple path right up to Anora's door. No one should really bother you or do much to stop you. There's a forcefield on the door though, so our rescue just got really complicated. Continue to follow the path down the hall to make it to the master bedroom and the entrance to the dungeon. Do not open the doors on the way there though. In the hallway with all of the rooms, there is a guard spending a little bit of time with one of the servants. He'll see through your disguise and raise the alarm. It won't cause you much trouble at this point, but it's completely pointless.
If you can, have your rogue pick the lock on the locked door on the way there. This should open up Howe's Treasure vault, which we obviously want to loot if we can. It's a tough lock to pick though, so don't worry if you can't do it. Keep an eye out for the Grey Warden Papers, which should be around here. Those papers will net us a special shield for Alistair from the Grey Warden Cache.
Advance and go into the dungeon. You should see Riordian, another Grey Warden, pull a bit of Captain Price on the guard. Go ahead and talk to our new friend and then head into the dungeon. You should change back into your regular armor automatically once you strike the first blow. You can do it manually if you want though.