This is the absolute first part of Dishonored. There are a few things to keep in mind when playing this area. Firstly, if you are planning a non-lethal playthourgh of Dishonored you cannot, even here, kill any enemies. There is a kind of secret in this area and an optional quest. This guide highlights all of these:
First to playing hide and seek with Emily under the bridge. Its fairly simple. Follow her there and use the stealth mechanic, on PC its pressing c and hiding behind some cover, for a little while, then pop out to get on with the quest.
The kind of secret is that you can drink the flask next to the posing man. I don’t know why you would, but you can.
Most importantly is how to defend the queen without killing any of the assassins. They are fairly easy to kill, one shot with your pistol or a few swings with the sword will suffice. To do this without killing all you have to do is block for a little while. On PC that is the Ctrl key. You won’t take any damage and the assassins disappear after a little while and you finish this part.