Escaping Vaas' camp with Grant is the first objective in Far Cry 3.
The two of you sneak through the camp, past caged prisoners, hanging prisoners, all manner of domesticated animals, a massive stack of luggage and passports, purses, and finally through the pirate's living quarters.
Sub-Objectives
Pick Up the Map and Phone
During the escape, you grab the map, lighter and phone from a table.
Heal Grant's Wound
During the end of the escape, Grant is wounded by Vaas.
This triggers a Quick-Time Event to heal Grant's wound.