By way of some random link-following (via), I ran across a review of K-ON, which mostly contained retelling. Such a style of review is usually incredibly dull, but I was grinning as every paragraph prompted me to recall the fun.
Yui, who has no musical talent, but was praised by her teacher in kindergarten for playing the castanets well, decides that a "light" music club could be fun. And of course, Ritsu needs that fourth warm body, so Yui is accepted. Thankfully, conveniently, Ritsu is a talented (if too enthusiastic) drummer, Mio is accomplished on the electric bass, and Mugi just happens to be an award-winning keyboardist. Yeah, I'll let it slide. Just go with it.
This is, of course, the cynical way to look at it. But you can just as easily think of the destiny throwing the four together, much like Aoi running into Kaoru in the Steel Caves of Tokyo. The choice is yours!
And that's really my one big complaint about K-On!...for a series about music, there really isn't a lot of music. Other than the OP and the ED, there are only three songs featured, and you only get full performances of two of them.
This is tantamount complaining that in a series about ballet, there's not a complete performance of Nutcracker and Swan's Lake in Princess Tutu. It's not as if Nodame included symphonies.