In X and Y, the Drives can be obtained by showing Genesect to a Hiker at the Fossil Lab in Ambrette Town. He says that he received the plans for the Drives from an acquaintance of his in Unova and made the Drives from them himself.
The four Drives appeared in Genesect and the Legend Awakened, each attached to a member of the Genesect Army (but not to the Red Genesect). While in the movie it was used with the same purpose of changing the type of Techno Blast, it was also the key item to tell each Genesect apart, with the one holding the Douse Drive having a different personality from its group.
It wasn't shown or mentioned in any point of the movie that Genesect could switch or take off the Drives.
In the manga
The Drives in Pokémon Adventures
In the Pokémon Adventures manga
From Mr. Perfect to Innocent Scientist, Colress used Genesect to battle against Blake. After falling for one of Blake's taunts, Colress angrily switched the Drive on Genesect's back for a Shock Drive in order to put Blake's Dewott at a disadvantage against the Paleozoic Pokémon. Once Blake had defeated and captured Genesect, he obtained the Shock Drive in the process.
The Shock Drive was later given to the Magician in order to reverse-engineer another set of Burn, Chill, and Douse Drives. Blake used the Burn Drive to battle Team Plasma on the Plasma Frigate, though, due to it being incomplete at the time, Genesect was injured by its own attack and left exhausted after using Techno Blast on some Team Plasma Grunts.
In Pokémon Adventures, the unnamed Drive attached to Genesect's back in called the Neutral Drive (Japanese: ノーマルカセットNormal Cassette).