Okay, firstly, I like to set the form action to <?=$_SERVER['REQUEST_URI']?> to submit it back to the current page, but leaving it as you have it will work fine too.
Secondly, you need to give all your <input>s a name attribute. This is the variable name that PHP will see.
When your users get an error (something doesn't validate correctly) you don't want all the data they entered to disappear. That means you have to set the value attributes of each input to what they had previously entered. Thus, your form starts to look like this:
<form action="<?=$_SERVER['REQUEST_URI']?>" method="" id="get-protected">
<div class="row requiredRow">
<label for="txt_FirstName">
First Name</label>
<input id="txt_FirstName" type="text" class="required" title="First Name. This is a required field" name="first_name" value="<?=htmlspecialchars($_POST['first_name'])?>" />
</div>
...
<div class="row">
<input type="submit" name="submit" value="" class="button" />
</div>
</form>
If you didn't know <?= is a basically a shortcut for <?php echo but it will only work if your server has short tags enabled. Some people prefer to type it out the long way (in case they want to switch servers later, or for future-compatibility, or because they're nutbars), but I say screw them, I'm lazy.
This page that has the form on it, has to saved with a .php extension (well, technically it doesn't have to, but that's another story). Then you need to handle you form validation. You have to code that up yourself. It might look something like this (put it above your form somewhere)
<?php
if($_POST['submit']) {
$errors = array()
if(empty($_POST['first_name'])) $errors[] = 'please enter your first name';
if(empty($errors)) {
// save the data to database or do whatever you want with it
header('redirect:succcess.php');
} else {
foreach($errors as $e) {
echo $e;
}
}
}
?>
It's been a while since I've coded in PHP so forgive me if there are syntax errors. That's the jist of it anyway, I'm sure you can find validation libraries out there if you Google. Might take some of the grunt work out of trying to validate email addresses and such.