How do I include a composer package into plain php?

After installing the package with composer, the composer has generated an autoloader that you can include with:

require_once 'vendor/autoload.php';

Then you can use the classes of the package without further includes. In your example this might be:

// Create an instance of WhatsProt.
$w = new WhatsProt($username, $nickname, $debug);

(taken from https://github.com/WHAnonymous/Chat-API/blob/master/examples/exampleRegister.php)

Note that this line from the example is not necessary, when you use the composer autoloader:

require_once('../src/whatsprot.class.php');