API Security

Hi,

I have a web application with just html and jquery (no asp.net nor any other framework)

Now I need to make an API to serve the webApplication and also the native phone Apps that will be built.
What simple API samples (prefer rest and json) can I follow to have a decent level of security? 

The Api will return some confidential user information.
I need to garantee that when I ask for user X information it will not be easy for someone else to get that same information
i.e the api will get information for user X only when acting on his behalf.

Thank you so much,

PangDev