Ralph certainly covered the structure of individual episodes: the patient's symptoms escalate; the team tries one treatment after another (with dramatic results, in some direction or another); House solves the case.
That's a fair description of the single-episode plotline, but there's a lot of other tools in the House arsenal - and ones which, I think, are more relevant to the show's fun and success then its bare-bones formula is.
Here's a few tools House uses which I think are worth taking note of.
Misanthropes are more interesting. House is a character crafted with the specific goal of causing conflict and tension wherever he goes, and whoever he interacts with. On the one hand, this is a lot of fun to watch - the malicious, snarky curmudgeon who does everything we'd never dare to do. On the other, more important hand - a character who causes conflict is a character who causes plot. A character like that is easy to bring into stories because he's willing to be outrageous, and because he actively encourages (or outright causes) the conflicts that create the plot. Notice how much of the plot consists of people telling House "no," and his attempts to get around them - his nature of head-butting others is what gives the story substance. Lesson to take home: create characters who can believably create conflicts or get involved in them - the bigger and more personal, the better. A trouble-maker is often a lot more interesting than a noble hero.
Get inside your characters' heads - by force, if necessary. It's often very difficult to do character exploration - it's tough to spotlight one character without ignoring the rest; often there's no good reason other characters should even know what's going on with the others; these are all particularly difficult in a series about medical professionals and a formula which doesn't really center around the characters at all. Luckily, House is a nosy bastard. And the writers spun that into "willing to do outrageous things to stay in the know"; "happy to blurt out embarrassing personal information to anybody and everybody"; and "tries to test his friends with convoluted behavior tests to understand their personality and motivations." That's not coincidence - again, this is a character deliberately crafted to serve and advance the plot (and the character arcs) in interesting, convincing ways. Lesson to take home: If character development is a goal of yours, be sure to have some element in the story that brings your characters' personality to the fore. If it's disconnected from the main plot, or purely reactive to it, it won't be interesting. Meddlesome characters are good tools for this.
Always have a goal. House is very good at having some big questions about the lead character juggling in the air at any given moment. It's also not shy about telling the viewers precisely what those questions are (the series, as its title character, is not known for its subtlety). "How far will House go in order to [get the girl/keep his team together/flip off a figure of authority/other]" is a common one. Other threads include "Why is House the way that he is?", "How is House affecting the doctors around him?", and others. These keep the viewers involved and curious - and rewarded when an arc does shed light on a certain point that's been built up. Lesson to take home: defining clear directions and mysteries to explore keeps viewers hooked - you're giving them something to look forward to, and presenting them with something mysterious and incomplete right now.
You've got to have a team. Well, not always. But House does - if he works in a vacuum, there's no show. So you've got to justify the team's existence, even though House is always the one who solves the case on his own. So, the series goes to great length to demonstrate that House instinctively needs a team, for feedback, brainstorming, and targeted mockery. That way, his need for a team - and his team in particular - becomes another facet of his complex personality, rather than an obvious plot device. Lesson to take home: When there's something you really need in order to tell a story, that might not quite fit or make sense - justify it; work its necessity into the very fabric of your writing; use this constraint and build upon it rather than accepting it as an unfortunate necessity.
That's what I'd take away from House. Hope this is helpful :)