Trying to write a REST API from scratch is not a simple task. There are many issues to factor and you will need to write a lot of code to process requests and data coming from the caller, authentication, retrieval of data and sending back responses.
Your best bet is to use a framework that already has this functionality ready and tested for you.
Some suggestions are:
Phalcon - REST API building - Easy to use all in one framework with huge performance
Apigility - A one size fits all API handling framework by Zend Technologies
Laravel API Building Tutorial
and many more. Simple searches on Bitbucket/Github will give you a lot of resources to start with.