I have never worked with APIs before (and have very little programming experience outside of HTML and CSS) and I am struggling to find any clear tutorials or explanations.
Woah I've heard this before. You dont want to rush into learning APIs, you need to get aquainted with a nice little programming language first. Once you have a little bit of programming skill the mystery of API will be revealed. Maybe give Ruby or Python a look as I've seen many people get started using those.
http://wiki.python.org/moin/BeginnersGuide
Oh and if you have a Mac or Linux based machine the best part is you probably already have Python installed!