To use jAPI in your project you will have to fallow a few steps only.
First download jAPI project source from this address .
Make sure that you included in your html page all scripts properly. You also have to include this two scripts in your html file: jAPI.js, jAPI-Remote.php.
jAPI-Remote.php actually can be any php script from which you want to use their server side methods.
You have to include jAPI-Core.php script in this file (jAPI-Remote.php) by adding this line of code at the beggining of your script:
include("httpHandler/jAPI-CORE.php");
And at the end of your script you will have to create a new instance of jAPI Base Class like this:
//all classes names comma separated as jAPIBaseClass parameter which you want to use
new jAPIBaseClass('YourClass,AnotherClass');
So, that's it!