PUT
$data = array('username'=>'dog','password'=>'tall');
$data_json = json_encode($data);
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_HTTPHEADER, array('Content-Type: application/json','Content-Length: ' . strlen($data_json)));
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, 'PUT');
curl_setopt($ch, CURLOPT_POSTFIELDS,$data_json);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$response = curl_exec($ch);
curl_close($ch);
POST
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_HTTPHEADER, array('Content-Type: application/json'));
curl_setopt($ch, CURLOPT_POST, 1);
curl_setopt($ch, CURLOPT_POSTFIELDS,$data_json);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$response = curl_exec($ch);
curl_close($ch);
GET
See @Dan H answer
DELETE
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, "DELETE");
curl_setopt($ch, CURLOPT_POSTFIELDS,$data_json);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$response = curl_exec($ch);
curl_close($ch);