Form data from index.php is sent to write.php, which processes the text into comma-separated values that are written to data.txt, the contents of which read.php reproduces in index.php.
There is also a cheeky little field in the form that appears 1000 pixels left of your viewport. You don't see it, but bots do, and if they put a value in that field, nothing is posted - it's primitive spam control.
I hereby publish this guestbook into the public domain. If you want to use and adapt it, go forth and be merry, no credits required - although a linkback would be a kind gesture in an otherwise unforgiving universe.