Amoeba obtains its food through the process of endocytosis.
Amoeba ingests their food by extending the pseudopods.
These extended pseudopods encircle and engulf live prey or particles and then forms a vacuole around them. This process is called phagocytosis or endocytosis.
Amoeba does not have a mouth.
When the particle is completely trapped the amoeba secretes digestive enzymes that digest the food.