The short: Same as Doom.
The longer: You (Gordon Freeman) work as an assistant at Black Mesa Research Facility where they perform various tests. At the beginning of the game, when you're helping out on one of these tests, an interdimensional portal appears to be ripped open, and aliens begin invading Black Mesa. At first, your goal is just to reach to the surface level and contact for help, but it becomes evident later on that the government is more interested in containing and silencing the events going on than rescuing anyone. You then are guided by other scientists to launch a satallite (sp?) up into space with the intention of closing the "portals" and then later, to reach a team of scientists who send you to the alien dimension to stop the 'source' of the alien invasion (of which include the Vorginauts). After defeating them, the G-man gives you a "thanks for being an unwitting pawn" speech, offers you a job, and you presumably accept it.
I'd suggest checking the article silent killa linked above though, as it'll describe it better.
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