Dishonored Walkthrough Part 10: The Royal Physician Part 4
When you're done looting everything, it's time to head into Sokolov Manor... and loot more things. You can usually find Sokolov in the lab on the rooftop, which is just about right next to you. There's just a lone guard between you and him; this problem can easily be solved with a crossbow bolt or a sleeping dart. Take him out, and use Blink to climb up and get into the lab. When you enter, loot the room for a Rune and choke out Sokolov. Now it's time to carry the guy back to the boat. This can be tough because of the numerous City Watchmen and maids wandering about, so if you decide to explore more you should be very careful.
There is a benefit or two to exploring a little more before making your exit. The first floor of the Manor contains a Sokolov Painting in the large art gallery. You can loot the area for more health, money and mana, too.
Now that it's time to escape, you'll be left with a few options. Dropping Sokolov in water will kill him, and falling from a great height will kill you both, so be careful of both. You can either head downstairs through the mansion, or take out the two guards in Sokolov's library hall. There's a secret elevator that necessitates a tank of whale oil to get going. You can find the spigot and tank dispenser in the lower laboratory. Note that you can also Blink with Sokolov; you can use this to get down the Manor's facade quickly, and head to the boat without being seen.
No matter how you get there, set Sokolov down on Sam's boat and speak with him to end the mission.