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.
API's aren't all that sophisticated. The word takes on mystical proportions.
Let's take a look at a specific API. For example, Twitter. Google Twitter API. First of the results is http://apiwiki.twitter.com/
You can find some Twitter API implementations in Python: http://apiwiki.twitter.com/Libraries#Python
Get Python. Get the API implementation. Start hacking.