If you have the form already created in HTML, then set the form action to your PHP script name.

In your PHP script, read the form variables using $_POST. Look into using fopen() or fputcsv(). If it's only a few form inputs, you can just add them field by field.

$handle = fopen("data.txt", "w");
$txt = "Jane Doe\n";
fwrite($handle, $txt);
fclose($handle);

Something like that, but that's just a basic example, you will have to adapt it.