Doctor Who: Every Character Who Can Fly The TARDIS
6. Leela
When it comes to piloting the TARDIS, Leela's level of skill is quite unusual.
She has plenty of courage and spirit, sure, but because she hails from a primitive human tribe, she isn't exactly the most intelligent of companions - so you'd think it would be impossible for her to even comprehend this complex time-travelling machine. And yet, she appears to be able to fly it quite well.
At the end of her introductory serial, The Face Of Evil, she rushes into the TARDIS and meddles with the controls, resulting in the ship dematerialising. While we don't see what happens immediately after this, the fact that the universe didn't implode must mean that she started up the TARDIS safely - so was this luck, or instinct?
This aside, a slightly more clear-cut example of Leela flying the TARDIS occurs in The Invisible Enemy. When the Doctor goes into a self-induced coma, she says "we'll take the TARDIS" to get help, and brings the Doctor back to his ship. The scene then cuts to a medical facility, with the TARDIS parked neatly in the background - and with the Doctor out of action, the assumption here is that Leela parked it herself.
Leela is a very curious individual - it was her who asked the Doctor if she could explore the universe with him - so it would make sense if she was interested in learning the TARDIS controls. Based on the results, it also seems like she's a fast learner!