After crushing, the olives are placed in woven baskets that are placed one on top of the other. The baskets (barely visible behind the rock wall) were then put under a large beam having weights tied to it in order to increase the pressure in squeezing the olives. See Here for a clear example of the use of such baskets.
The oil and water were then collected in the hewn basins beneath the baskets.
Some have suggested that the "object" carved into the wall, between the two presses, might be a representation of an Idumean (Edomite) deity.
This oil press was found in a repurposed cistern at Maresha/Marisa. It dates to the Hellenistic Period (ca. 3rd-2nd centuries BC). Over 20 such presses have been discovered at Marisa.