Background
I have no idea how to use an API.
I know that all APIs are different, but I've been doing research and I don't fully understand the documentation that comes along with them. There's a programming competition at my university in a month and a half that I want to compete in (revolved around APIs) but nobody on my team has ever used one. We're computer science majors, so we have experience programming, but we've just never been exposed to an API. I tried looking at Twitter's documentation, but I'm lost.
Would anyone be able to give me some tips on how to get started? Maybe a very easy API with examples, or explaining essential things about common elements of different APIs? I don't need a full-blown tutorial on Stack Overflow; I just need to be pointed in the right direction.
Update
The programming languages that I'm most fluent in are C (simple text editor usually) and Java (Eclipse). In an attempt to be more specific with my question: I understand that APIs (and yes, external libraries are what I was referring to) are simply sets of functions.
Question
I guess what I'm trying to ask is how I would go about accessing those functions. Do I need to download specific files and include them in my programs, or do they need to be accessed remotely, etc.?