If you aren't familiar with how to use WebAPIs, you may want to start with some simple APIs to get an understanding of how they work. The way you use them is basically the same in any programming language.
In Mathematica, you'll want to use the URLExecute function:
http://reference.wolfram.com/language/ref/URLExecute.html
There are examples on that page of how it can be used with other APIs.
