Having been bushwhacked by Elizabeth and tossed out by Daisy Fitzroy, you'll soon have a chance to help Booker regain some of his pride. Starting from Finkton Docks, enter the Delivery Center to your left and grab the Voxophone on the floor between a pair of desks.
Continue through the docks in search of Elizabeth but keep an eye out for an Employees Only door near the end of the pier. This one leads to an office with a Gear inside. You will encounter fierce resistance from both human and machine as soon as you try to leave the office. Possess the Mosquito machines to make them yours. Follow the objective marker and pry the door open.
Now, keep pursuing Elizabeth through the harmless dimensional tears, and once she gets nabbed, check the desks behind the partition on the left side to find a Voxophone. Follow the objective arrow to the sky-line. Explore the port, kill enemies and leave Elizabeth to rot in her cell for a while longer. Look for is a pair of large, red double doors that leads to a cell block with an Infusion phial.
Go on to where Elizabeth is being held and rescue her, only to realize that she's capable of freeing herself... Navigate along the sky-line to the next objective and watch some events unfold.
Booker regroups with Elizabeth afterward. Step onto the trolley to find a telescope. The door to the cabin requires 5 lock picks to open and has a Gear inside. Leave the Docks for the Finkton Proper.