How to use CleanTalk in a direct PHP site?

I’m trying to support a website that has a handwritten contact form that uses PHP. This website is not powered by WordPress/Drupal/etc. so none of the plugins can be used. I simply can’t wrap my head around how to get CleanTalk to work!

–> Can anyone point me to complete demo PHP code? Just a form-to-email submission where CleanTalk is included.

– The code samples over at https://github.com/CleanTalk/php-antispam#sample-spam-test-for-text-comment are apparently not complete because if I drop that code into a blank index.php page (and enter my own API key) then it doesn’t work: there is a form and I can submit it, but the result is a blank page, and I don’t see where to specify a recipient for the form result either.
– The provided example.php doesn’t even load, it gives a HTTP error 500.
– The other provided tool (here: https://github.com/CleanTalk/php-uni#php-uni) contains a neat installer, but the result after running that installer is incomplete PHP code added to the index.php file.
– In each case I can’t see what more needs to be done. HELP!

Your kind help is sincerely appreciated!
Greetings from Austria,
Ben