Have six villagers build a storage pit about 3 squares from the elephant. Make sure that the 6 villagers are roughly equidistant from the elephant. In particular make sure that no one villager is too far out in front of the others. Select all six villagers and then click on the elephant.
Gazelle hunting is significantly harder than elephant hunting. I recommend ignoring gazelles initially. Alligators and lions are quite unattractive as a food source. They bite back, offer little food, and decay quickly.
Shore fishing is the fastest means of collecting food. Use one villager
per school of shore fish. It is worth placing a villager on a
school as much as 7 squares away from the nearest food collection
point (town center or storage pit).