They don't “move” after they've passed through their free-floating larval stage and have attached themselves to a piece of rock or coral. They stay in the same place the rest of their lives. read more
The anemone will move around the aquarium until it finds a spot with the right light and water current. If it crosses a filter intake it can get all or partially sucked in and killed. Sea anemones can also reproduce asexually by pedal laceration. read more