Using a REST API can be as simple as opening an URL in your browser. More examples on that here: http://lithosphere.lithium.com/t5/Support-Knowledg
Restful APIs are a general concept and there are some examples explaining the concept and working with them on the web, e.g. here: http://www.peej.co.uk/articles/restfully-delicious
Feel free to share a more specific Lithium REST API question once you've played around a bit.
Principal Technical Consultant
Lithium Technologies, Inc.