Primary access is by boat. The hydrofoil and ferry operators SIREMAR Ustica Lines ,and NGI all connect Lipari to other points in the Aeolian Islands and to Sicily and the mainland. If you're not bringing a vehicle, try to board a hydrofoil; they're significantly quicker than the ferries, and generally quite comfortable.
Air Panarea offers helicopter flights to Lipari on Mondays, Wednesdays and Fridays during the summer. However, they're expensive and don't save much time compared to the hydrofoils