We can't send post fields, because we want to send JSON, not pretend to be a form (the merits of an API which accepts POST requests with data in form-format is an interesting debate). Instead, we create the correct JSON data, set that as the body of the POST request, and also set the headers correctly so that the server that receives this request will understand what we sent.

She includes a code example (about ten lines) showing the POSTing process that sets up options using curl's curl_setopt. Be sure to set up the headers to send as "application/json" - that's the trick to letting the remote end know the format.

I recently wanted to perform a HEAD request to a file, after which I wanted to perform some more advanced HTTP interaction, so CURL was also the tool of choice here.

He started with the (slow?) command line to get the parameters right before moving into PHP. After picking out the right ones ("curl -I -X HEAD http://localhost/admin/") he transfers them into a series of curl_setopt calls that specifies a HEAD request type and no content to send (with CURLOPT_NOBODY).