Navigate to the Vehicles Menu from the Main Menu on the left
Click on the vehicle's name, taking you to that vehicle's overview page
Click on the downward facing arrow next to "Edit" in the top right corner, select "Publish"

Please note, the following is required to publish a vehicle:
At least 1 Photo
VIN
Description (located at the bottom of the "Details" tab)
Base Price Set (Prices tab)