Upwards of five times today I have attempted the first mission of Dishonored, and five times I've been foiled by the game. Each time, I've taken every measure to avoid detection, and avoid accidental killing. In addition, I leave no unconscious bodies to be discovered. The problem is, every time I finish the mission, I've apparently either been detected, or have killed someone. Apparently. What am I supposed to do about this? To the best of my knowledge, I was never detected, nor did I kill anyone. I just don't understand. Help would be greatly appreciated.

Not sure about detection, but as for kills.... did you accidentally drop anyone into water? And did you kill the 2 assassins during the intro (the ones that attack the empress) ?

For detection, see in the Notes on Stealth and Detection sticky for possible help... myself, I got the Ghost for the mission, but I'm still not sure how exactly...

Well one mistake I made when I attempted non lethal the first mission was putting unconscious bodies into the dumpster right next to the wall your supposed to blow up. Explosion killed the bodies.

Just discoevered that every single time I set the explosive off, it automatically flashes up that I've been seen, no matter whether I'm in sight or not.

K.O. the two guards near the explosive, and place them in the hollow container near the door. K.O.-ing people does not count against the G.g.g.g.g.host rating of a given mission.

Yeah the tricky part is the door you have to blow up.

Using the pipes you can safely land undetected in the room, but you still have to KO the two guards there, or they will immediately spot you when the door explodes. You may leave anyone awake in the previous room, it doesn't matter as long as the second door is closed.
Put the two knocked out guards somewhere safe, not close to the door you're planning to blow up.

The nextr tricky part is actually jumping in the water. You have to jump right off, not go down on the stairs. Swim underwater until you're right in front of the sewer tunnel entrance, as being too far, or too near, will get you detected by the guards on the wall.
This is honestly the trickiest part, but since they are looking at the stairs you would probably have taken, in a cone fashion, you want to be on their sides. Not sure I'm making myself clear, but here you go.