The story of FLCL isn't too complicated when you break it down and honestly it's not that important since the show is more about being a metaphor for puberty than anything else. You'll have to be more specific about what you need help understanding exactly but the basic jist is this:
Haruko is an alien looking for Atomisk the pirate king (I can't quite remember if it's because she loves him, because she wants to absorb his power, or both).
Medical mechanica is an evil interplanetary corporation. They've captured Atomisk. They want to rid the universe of all though or something.
Haruko is using Naota's head as a portal to pull MM robots out to try and free Atomisk.
That's all that really matters as far as "plot" elements are concerned. As I already said the show is more about the themes than any of that.