No, you don't need any sort of database for this (though in the long run it's something to consider).
Not counting the site layout and form design, you've got three parts to do.
1) Get the information from the form. There's a tutorial in the manual on this subject; basically, everything that is submitted in the form will appear in the $GET or $POST array depending on which method you use in the <form> tag, and named according to the names that you used in the form fields - so a <input type="text" name="foo"/> would create an entry named $_POST['foo'] in the script that is processing the form.
2) Validate the form data. If you want to be wild and reckless you can leave this step out, but there's no better time for getting into good habits than at the beginning. Basically, make sure that what is being submitted is sensible. If a field has to be part of the submission, make sure it's there using [man]isset[/man]. If it has to contain a value, make sure it's not [man]empty[/man]. Do this at the very least.
3) Update the text file. You'll need to work out some sort of format for this: how you are going to write the form data in the text file, how you are going to separate one item from the next, and so on. PHP's got a bunch of filesystem functions to use: [man]fopen[/man], [man]fwrite[/man], [man]fclose[/man], and so on. Because you want to add the latest text to the top of the file what you'll need to do is read the whole file (the [man]file_get_contents[/man] function makes this a one-step process); then overwrite the file with the next text, and tack the text you just read in on the end. ([man]file_put_contents[/man] will make this a one-step process if you're using a sufficiently recent version of PHP, otherwise, you'll need to use fopen($the_filename, 'w'), fwrite() the new text, fwrite() the old text, then fclose(). Or if you wander over to the Code Critique forum, you can find rpanning's file_put_contents emulator.
