This is my very basic demonstration system:
http://www.youtube.com/watch?v=c7tlgqzmQmM
It goes over the components of what you'll need. Sizes vary, of
course. The demo system is only 5 gallons of fish tank, so you'll probably want to build something larger eventually.
AP has 4 fundamental components: a fish tank, a grow bed, a
pump, and symbiotic bacteria that convert fish waste (ammonia) to plant food (nitrate).
For me there is nothing quite like doing, so I always recommend setting up a small system to help you understand how the pieces fit together. Experiment small, then build big.
Oh, and generally
solar and inexpensive don't go together unless you are able to source
free solar parts.