The route into the TARDIS can be a surprisingly common one, if you happen to be (or have been) female, youngish, human and British during the last 50-odd years of Earth history. All you have to do is wait for an alien invasion of some sort, and keep your eye out for a big blue box. If you see one, chances are there will be an eccentric man somewhere in the vicinity, barking strange orders and running about.
Now, here comes the tricky bit, you need to make yourself useful to him, and sort of insinuate your way into his attention. This can either be because you need saving from the aliens and he can’t resist a damsel (or mansel) in distress, or because you’re in a position of authority and he needs you to do what he says right away. It might help to see if you can join your nearest branch of UNIT, or, if you’re a journalist like Sarah Jane Smith, just barge your way in and start asking questions until you and he are face to face.
What you need to do is be ready to be won over by him, be enchanted by his personality, and then occasionally bring his rampaging ego up short. It’s a bit like looking after a toddler, if a toddler had access to weaponised Lego.
The best part is that the post starts off with this phrase:
"Note: this is not a guide for budding actors and actresses, on how best to audition for the role of a companion on Doctor Who.”