Most of the time when I work with APIs from PHP, I use Guzzle - it's awesome and modern and elegant. However some of my work is with legacy platforms and I recently had a situation where we needed to integrate with a API using OAuth2, and launch that integration before the planned platform upgrade from an older version of PHP was expected to complete.

(this drives me nuts, I love upgrading systems but the downside is you have to work with the old ones first and none of the tools you want have been invented yet!)

For OAuth2, all I had to be able to do was to send an Authorization header with my web request from PHP. My second-favourite way of making API calls from PHP is to use PHP's stream handling, so I did that. It's not code you see very often but it's super-simple and it works on every PHP platform I've tried so far, so here's an example:

// assemble the options
$opts = array(
  'http'=>array(
    'header'=> "Authorization: Bearer " . $access_token
  )
);
// create the context
$context = stream_context_create($opts);

// now make the request! Use the context and simply output the result
echo file_get_contents('http://api.example.com/endpoint1', false, $context);

If you're trying to make an API call from PHP and installing better tools is hard for any reason, this example may help!