Susan Foreman (Carole Ann Ford) a 15-year-old student at the Coal Hill School, Shoreditch, London, is attracting the puzzled attention of two teachers--Ian Chesterton (William Russell) and Barbara Wright (Jacqueline Hill). The girl has knowledge of Physics and History far beyond her years. They follow her home to a junkyard at 76 Trotter's Lane, where a blue Police Call Box is humming. They meet her Grandfather (William Hartnell), who orders them to leave.
Ian and Barbara are certain that something is up, and they fear Susan is being held against her will inside the box. They push inside, where they discover that it is bigger on the inside than the outside. Young Susan calls it a TARDIS (Time and Relative Dimensions in Space); in fact, the term was invented by the actress Carole Ann Ford herself. Everyone in Britain, when they discover a surprisingly large room in a small cottage, call it a TARDIS. It is in fact a ship which can travel anywhere in time and anywhere in space. The Doctor has stolen it.
He and his Grand-daughter are from the planet Gallifrey, where the immensely powerful Time Lords have ruled for millions of years--though it is many episodes before this information comes out. In the pilot, Susan tells them she was born in the 49th Century, but this does not happen in the official first episode. The Doctor is a prickly character--irascible, sarcastic, insulting, quick to anger, and dismissive of the intellectually inferior Human species. We love him on sight--at least, I did--and it is only after many episodes of the longest-running SF show on TV that we realize he is quite fond of us as well. Or perhaps a few hundred more years of travel have mellowed him somewhat.
In any event, the argument over whether time-travel is a reality beyond the comprehension of human beings or a ridiculous fantasy is settled in a practical manner as The Doctor engages the TARDIS and--kidnapping Ian and Barbara in the process--transports them all to Earth in the Palaeolithic Age. The strange sound the TARDIS makes as it appears and disappears is the sound of space-time being ripped apart, made by a key on piano-strings in a back room at the BBC. Ian is still not convinced they have travelled through time. "Open the door, Doctor Foreman," he says, and the doctor replies, "Doctor Who?" In fifty years on the BBC, no-one has ever spoken The Doctor's real name. We don't know what it is. In the 1996 TV-movie, a character called him Doctor Who. That's just sloppy writing.
The four chrononauts step out onto a cold, barren landscape. The Doctor and Susan both remark on the fact that the TARDIS is still a blue Police Box and wonder why it hasn't changed. Later, we will learn that the Chameleon Circuit, which is supposed to change the outward form of the TARDIS to something unremarkable in the time and place where it has landed, is broken. That and the fact that it is constantly turning up in the wrong time and place leads me to believe that The Doctor has stolen a defective TARDIS. Perhaps that is why he got away with stealing it.
The Doctor, wandering around the landscape, takes out his pipe and lights it. A caveman, on a quest for fire, knocks him on the head and takes him away, setting in motion the basic plot of the story--only the one who can make fire can be the leader of the tribe. The four time-travellers spend the rest of the serial caught up in Palaeolithic fire-politics and indulge in the standard Doctor Who round of fleeing, hiding, being captured and imprisoned, escaping and fleeing again. Finally, they get back to the TARDIS and take off for 1963 London, but end up on the planet Skaro, where the Daleks live.