Season 1, Episode 1, Part 1: An Unearthly Child

The start of something wonderful.

After some titles that try far far far too hard to be sci-fi (poorly-sequenced synth and everything), we fade in to a policeman, investigating what seems to be a junkyard, where all petty crime takes place. The policeman, who is exceedingly British, happens upon a police public call box. For the record, and because you'll be hearing about it a lot, a police public call box is like a phone booth, but only for calling the police, and is not in fact what this phone box actually is (more on that later). There were apparently an awful lot of them around London and its environs in the 1950s, so it probably wouldn't appear terribly out of place in 1963, when this episode is apparently set (for lack of a better choice).

After this bewildering opening, we dissolve (I'm detecting a theme here) to Coal Hill School, and find two teachers, a man and a woman, talking in a stereotype lab.

Our heroes.

They discuss the problems they're both having with Susan Forman, a 15-year-old girl, and the film shows its age by randomly dimming a bit. Apparently, Susan knows far too much about science and history and far too little about everything else (she's unfamiliar with the British monetary system, and the show manages to accurately predict England going decimal), and has either a very strange upbringing or some strange social anxieties.

Our heroine.

Conversation suddenly turns to Susan's grandfather, who seems to live at the junkyard we saw earlier - it's listed as Susan's home address. The socially responsible teachers decide to stalk the young girl (who dresses like a Star Trek extra). As they talk to Susan, we find that the teachers are called Mr. Chesterton and Ms. Wright. They lend her a book about the French Revolution, aptly titled "The French Revolution," which she begins to read with a critical eye as the creepy teachers stake out the junkyard until she arrives.
The junkyard, which is conveniently full of old theater props (the BBC loves saving money), still contains the police box, which they note is out of place and is gently thrumming. An old man in an odd mode of dress (William Hartnell in a fur hat, frock coat, and a thin scarf) enters; they pointlessly hide, then attract his attention when he goes to step into the box.

Our hero.

He refuses to show them the inside of the box, about which he is rather rude; they surmise that Susan is locked up inside after hearing her voice calling out for "grandfather." As the teachers turn to leave, Susan opens the door, and Chesterton and Wright bull their way into the box, which (thanks to clever cuts) is much larger on the inside, and far more futuristic: the walls are covered in circles, and some sort of hexagonal console in the center takes up space, covered in switches.

The future is CIRCLES

Chesterton demands an explanation; after a bit of blithering, Hartnell looks directly at the camera and says "You don't understand, so you find excuses."

Everyone else wonders just what Hartnell is staring at.

Then continues to explain that the larger-on-the-inside phone box is just a marvel of technology that Chesterton doesn't, and can't, understand: it's a ship, called the TARDIS (standing for Time And Relative Dimension In Space, for some reason), and can go anywhere in time and space. Hartnell emphasizes that the teachers are like children to him, and that children from his planet would be insulted by the comparison. He then declares that they're coming along; they can't tell the world, despite Susan's protests that "Their minds reject things they don't understand" (such wonderful social commentary).
As the teachers try to leave, high-pitched sound effects start up, Hartnell brags and chuckles, and proceeds to punish Chesterton with an electric shock when he touches the console. What a nice guy he is. Promising to open the door so that the teachers and Susan can leave, he instead starts the machine; bits start oscillating, a noise like a crosscut saw going through wood (slowed down) plays, and various effects start up as, on a monitor on the wall, London recedes into the distance.

The TARDIS takes off through time and space. You'll just have to trust me on this one.

We fade in on the TARDIS sitting in a desolate wasteland, which fans will know as the BBC quarry (a popular hole in the ground for filming scenes such as this). The teachers lay on the floor of the TARDIS as, outside, a shadow approaches and stands around sinisterly through the credits.

So that's a recap. Now the actual review, I suppose...
Well, for starters, the Doctor is kind of a dick. If I didn't know where this show was going, I probably wouldn't keep watching, but I may be overestimating the quality of all the other programming available in the 1960s. The fade-in fade-out special effects we're treating to look like somebody messing with a paint mixer and a lava lamp, and we were treated to all of 4 sets, including the interior of a car. Not a great start for one of the best sci-fi series ever broadcast.

Cutting-edge effects, indeed. Things will get better, in 45 years or so.