Kei Kusanagi has a mysterious disease which gives him "standstills". If he doesn't fight to keep himself going at all times, he's liable to go into a coma and not wake up or even physically age for hours, weeks or on one occasion even years. He looks fifteen years old, but unbeknownst to everyone but his uncle and aunt he's really eighteen.
Mizuho Kazami is the local school's pink-haired and curvaceous new teacher. She's also an alien whose UFO's arrival was accidentally witnessed by Kei. On her first day at school she confronts him in the gym supply closet, after which a chain of bad luck leads to them being discovered there and their headmaster jumping to unfortunate conclusions. Fortunately a lie is invented to save Mizuho's fledgling teaching career. Mizuho and Kei must pretend to be married. Kei's really eighteen, remember?
That's right, it's one of those anime. Forget superhero comics. This must be the ultimate wish fulfilment scenario... you're fifteen years old, but you're secretly married to your smokin' hot teacher although you can't tell anyone. Yup, it's another Magical Girlfriend anime, except that this time the "magic" is alien technology. It's a fairly standard example of the genre, adhering to most of the formulae and throwing in plenty of embarrassing coincidences. Your reaction to the show will depend on whether you can get past that and commit emotionally to the characters, which is a prerequisite for enjoying a romantic comedy like this.
This probably sounds groanworthy and Please Teacher certainly knows what kind of pervert it's aiming for. However on another level, the show tramples all over the usual fantasies. Magical Girlfriend anime usually gloss over the awkwardness and downsides of being thrown together with a complete stranger, but this series isn't afraid to show us the problems facing Mizuho and Kei. They may be fated to be together, but that doesn't stop them quarrelling, having misunderstandings and making a mess of their private and school lives alike. They doubt each other. They have to work through their issues. Personally I found this far more mature than nonsense like Oh My Goddess, in which everything is perfect and lovey-dovey and the only obstacles to happiness are contrived external ones.
That's a slightly surprising focus for a show of this genre, but fortunately the characterisation is good. Mizuho can be confused, petty and insecure. Kei is struggling with a medical condition that's already wrecked his life once. The supporting cast are particularly strong... not comedy whackos (this isn't that kind of anime) but real people who can make a godawful mess of their love lives. Again, this show is more mature than you'd think. No one's the Comedy Relief, or the Gay One, or the Gratuitous Bitch Who Gets Her Comeuppance. Yet again, this show is taking its loser-pleasing central concept far more seriously than you'd expect.
Even its SF elements (spaceships, aliens, teleportation) don't stop this show from feeling oddly realistic. It's a romance, yes, but it's driven by its cast's personal problems and character flaws. Being a short series (12 episodes instead of 26) it has a relatively well-constructed plot, but if you want to return a year or two later, there's the Please Twins spin-off series.
Unfortunately there's also the OVA episode. It's cheap, sleazy and adds nothing to the TV series, which already had a satisfying end with no plot threads left hanging. Liberated from the restrictions of television it overdoes the fanservice, which one expects from OVAs but not to this extent. Seeing Kei and Mizuho having sex would have been more meaningful if they hadn't already consummated their relationship offscreen a few episodes before. I used to hate this episode. However I've since discovered that it stands up surprisingly well to rewatching. It's funny. If you can forgive its foibles there's fun to be had here, though you won't miss much if you skip it.
Curiously, despite being voiced by Kikuko Inoue (mmmm...) I found Mizuho oddly unsexy. She's more like a big sister. Her real and cover professions are both paternalistic, one being "high school teacher" and the other being to observe Earth for the Galactic Federation. I wouldn't kick her out of bed or anything, but it's another example of how this show panders far less than you'd expect from a one-paragraph description.
It's still a Magical Girlfriend show, though. More clear-eyed than much of the genre, but not exactly subversive. It's heartwarming and can even be poignant, but many people haven't been able to get past its far-fetched premise and the fact that it adheres to the genre's formulae. I couldn't recommend it to anyone who didn't already like this kind of thing, but I think it's underrated.