How to pull of a RESTful URL the right way

I am having difficulty in how to proceed in making a website that uses a RESTful URL architecture. There are a lot of website tutorials saying that they have made a RESTful URL and what more you can do but none of them go into detail as to how they have managed to go from:

example:

http://ift.tt/2h75xDf

to

http://ift.tt/2gbBVHv

My understanding of the URL is that it is a path to the file being used, e.g. The properties.php file is being used above. But how can I get the second URL above without explicitly making a properties folder and then a file named 235?

What is the best way of achieving this and/ or the best API to use?

This has been boggling my mind for a while now and there doesn't seem to be a simple - do this - answer to the question.