A remote control is a hand-held device for controlling mechanisms across a varied distance, predating voice-command technology.
In 2152, Malcolm Reed used a remote control to detonate, from the bridge of Enterprise, an explosive device near a group of warp plasma canisters aboard an automated repair station. (ENT: "Dead Stop")
Later that year, Charles Tucker III used a small remote control to ignite a series of exposed well heads for deuterium pumps, thereby trapping a group of Klingon pirates in a ring of fire. (ENT: "Marauders")
A remote control was used by Enolian guards in 2152. Used to operate sets of handcuffs, it could release the restraints or cause them to electrocute their wearer. This type of device additionally doubled as a communicator. (ENT: "Canamar")
The next year, Lieutenant Reed used a remote control, while standing on the transporter platform aboard Enterprise, to detonate several charges which were connected to the EPS manifold aboard the transport Arctic One, destroying that vessel and Borg drones which were on board. (ENT: "Regeneration")
In a holographic program set in 2161, Charles Tucker III used a remote control to trigger a fake Tenebian amethyst so it suddenly started emitting a rapid series of bright flashes, momentarily blinding a gang of aliens on Rigel X. (ENT: "These Are the Voyages...")
In 2270, an Orion lieutenant offered to rig a remote control device to detonate dilithium explosives on an asteroid's surface. The captain declined, saying he wanted to see the look on Kirk's face when he informed him of their mutual demise. (TAS: "The Pirates of Orion")
In 2376, B'Elanna Torres gave a television with a remote control to Tom Paris as a gift. Although she attempted to give the TV set a 1950s authenticity, remote controls were not available with TV sets until the early-1960s. (VOY: "Memorial")
Both Doctor McCoy (2268) and Ensign Nog (2374) operated neural stimulators by remote control to give motion to mindless bodies; Spock's brainless one (TOS: "Spock's Brain") and Keevan's corpse (DS9: "The Magnificent Ferengi") respectively.