I don't think it's too complicated at all. The voiceover Amy did for Series 6 on BBC America is a pretty good description:
When I was a little girl, I had an imaginary friend. And when I grew up, he came back. He’s called the Doctor. He comes from somewhere else. He’s got a box called the TARDIS that’s bigger on the inside and can travel anywhere in time and space. I ran away with him, and we’ve been running ever since.
Series 6 itself, however, did get a bit bogged down in continuity. Series 5 is a pretty good jumping on point, though.