On this page of our guide to BioShock Infinite you will find the first part of a detailed walkthrough of Chapter 36 - Hand of the Prophet. On the way to the interactive barge the characters have to fight, but there is also a chance to explore the area and find an easy to open safe. The barge will head towards the Comstock airship.
Once you've left Comstock's house search the room you're currently standing in very thoroughly and then ask Elizabeth to break a lock on a door leading to the roof. Go there and expect to take part in a new battle.
Pods with Mechanized Patriots will land on the roof and you'll also have to deal with standard soldiers. Make sure to exploit nearby tears to aid you in the battle, especially since they can be used to summon a rocket automaton and a Mosquito.
Search the roof after you've won the battle. There is a new lockpick next to a dead policeman to the left of the building with closed doors.
Break into the building mentioned above (the lock requires you to have 3 lockpicks) and check the left room to uncover Voxophone #77 on a stack of documents.
You can find 2 additional lockpicks in front of the barred elevator in the main corridor.
There is a safe in a room with a hole in the wall. Opening the safe requires only 1 lockpick and it should contain about 100 silver eagles. Once you've searched all the rooms and interacted with the machine used to upgrade vigors head outside and proceed towards the moored barge.
Make sure to unlock a nearby Vantage point #37 - Telescope before entering the barge (this is the last vantage point in the game).
Once you're ready to move on with the mission enter the barge and start it by pulling a lever located at its beak. The barge will automatically set course towards Comstock's zeppelin. Notice maintenance hooks on this barge. An air battle will begin soon and that's when they will come in handy.