Jellyfish, like their relatives, the sea anemones, are all carnivores. Depending on the species and its size, they can feed on anything from tiny zooplankton to small fish. The stinging cells, that when discharged are involved in prey capture, are produced by the jellyfish animal itself by specific cells called nematocytes. When thinking about the anatomy of a jellyfish, think of it as an upside down anemone that is not attached. The mouth, would therefor be located on the underside, centered among the ring of tentacles.

It depends on the species of jellyfish.Some eat small zooplankton, others eat fish.
Jellyfish have something called a nematocyst. It's like a harpoon that shoots out and injects a small amount of venom into the prey. Jellyfish are closely related to sea anemones, which also sting the same way.
Jellyfish don't have a mouth like we do. They sting their prey and then bring them directly into their central cavity- like a stomach. Inside the cavity they secrete juices and the food slowly is digested. Like the scene from Star Wars: Return of the Jedi.