Well, I think one problem I had were the file permissions. But I have set those to '0666'. Then I actually got the script to work. It saved a file with the new contents on top, just like my PHP should do.
But then I manually reuploaded the .txt file via FTP. Looking back in my cPanel account I can see that the file permissions are '0666', but for some reason, my script seems to be hanging....
My site uses AJAX to send and get information, and when I try to run this, the loading page comes up and never goes away. I'm not sure why, but for some reason it seems the script is executed, but then something happens and it never finishes.
I have slightly modified my code since my original post, so I'll post that code here. But the code still should work, it is probably just an issue now of letting the server sync with my files and permissions.
<?PHP
$getName = $_POST['name']; // Gets the user's name
$getInfo = $_POST['message']; // Gets the new info
$Months = array("January","February","March","April","May","June","July","August","September","October","November","December");
$tagInfo = "<div class='smallTitle'>" . $getName . " - " . $Months[date("m")-1] . " " . date("d") . ", " . date("Y") . "</div><div class='contentText'>" . $getInfo . "</div>";
$tagBook = file_get_contents("tagBook.txt") or exit("Unable to open file for reading!");
$tagBook_file = "tagBook.txt";
$fp = fopen($tagBook_file, 'w') or exit("Unable to open file!"); // Opens the file for additional info
fwrite($fp, $tagInfo . "<br>" . $tagBook); // Writes the new info to the file
fclose($fp); // Closes the file
echo "http://sup3rkirby.zeeblo.com/tag/tagBook.txt;
?>