You can enable the CURLOPT_VERBOSE option and log that information to a (temporary) CURLOPT_STDERR:

// CURLOPT_VERBOSE: TRUE to output verbose information.
// Writes output to STDERR, 
// -or- the file specified using CURLOPT_STDERR.
curl_setopt($curlHandle, CURLOPT_VERBOSE, true);

$streamVerboseHandle = fopen('php://temp', 'w+');
curl_setopt($curlHandle, CURLOPT_STDERR, $streamVerboseHandle);

You can then read it after curl has done the request:

$result = curl_exec($curlHandle);
if ($result === FALSE) {
    printf("cUrl error (#%d): %s<br>\n",
           curl_errno($curlHandle),
           htmlspecialchars(curl_error($curlHandle)))
           ;
}

rewind($streamVerboseHandle);
$verboseLog = stream_get_contents($streamVerboseHandle);

echo "cUrl verbose information:\n", 
     "<pre>", htmlspecialchars($verboseLog), "</pre>\n";

(I originally answered similar but more extended in a related question.)

More information like metrics about the last request is available via curl_getinfo. This information can be useful for debugging curl requests, too. A usage example, I would normally wrap that into a function:

$version = curl_version();
extract(curl_getinfo($curlHandle));
$metrics = <<<EOD
URL....: $url
Code...: $http_code ($redirect_count redirect(s) in $redirect_time secs)
Content: $content_type Size: $download_content_length (Own: $size_download) Filetime: $filetime
Time...: $total_time Start @ $starttransfer_time (DNS: $namelookup_time Connect: $connect_time Request: $pretransfer_time)
Speed..: Down: $speed_download (avg.) Up: $speed_upload (avg.)
Curl...: v{$version['version']}
EOD;

Here is a simpler code for the same:

   curl_setopt($ch, CURLOPT_VERBOSE, 1);
   curl_setopt($ch, CURLOPT_STDERR, $fp);

where $fp is a file handle to output errors. For example:

   $fp = fopen(dirname(__FILE__).'/errorlog.txt', 'w');

( Read on )

Here is an even simplier way, by writing directly to php error output

curl_setopt($curl, CURLOPT_VERBOSE, true);
curl_setopt($curl, CURLOPT_STDERR, fopen('php://stderr', 'w'));

To just get the info of a CURL request do this:

$response = curl_exec($ch);

$info = curl_getinfo($ch);
var_dump($info);

If you just want a very quick way to debug the result:

$ch = curl_init();
curl_exec($ch);
$curl_error = curl_error($ch);
echo "<script>console.log($curl_error);</script>"

Output debug info to STDERR:

$curlHandler = curl_init();

curl_setopt_array($curlHandler, [
    CURLOPT_URL => '
    CURLOPT_RETURNTRANSFER => true,

    /**
     * Specify debug option
     */
    CURLOPT_VERBOSE => true,
]);

curl_exec($curlHandler);

curl_close($curlHandler);

Output debug info to file:

$curlHandler = curl_init();

curl_setopt_array($curlHandler, [
    CURLOPT_URL => '
    CURLOPT_RETURNTRANSFER => true,

    /**
     * Specify debug option.
     */
    CURLOPT_VERBOSE => true,

    /**
     * Specify log file.
     * Make sure that the folder is writable.
     */
    CURLOPT_STDERR => fopen('./curl.log', 'w+'),
]);

curl_exec($curlHandler);

curl_close($curlHandler);

See

Another (crude) option is to utilize netcat for dumping the full request:

nc -l -p 8000 -w 3 | tee curldbg.txt

And of course sending the failing request to it:

curl_setup(CURLOPT_URL, "");

Notably that will always hang+fail, since netcat won't ever construct a valid HTTP response. It's really just for inspecting what really got sent. The better option, of course, is using a http request debugging service.