You wanna change your query to...
$sql = mysql_query("select * from $tbl_name WHERE first_name LIKE '%". $input . "%'");
But you really shouldn't be using mysql_*, its deprecated, you should use PDO to connect to the database
EDIT...
Your form has a method of "post" so you should have this instead...
$input = $_POST['find'];
I believe that will solve your problem! :)
EDIT 2...
Ok you need to find out why your form isnt posting the variable... So just have this on the page...
<form name="search" method="post" action="process_search.php">
Seach for: <input type="text" name="find" />
<input type="submit" name="submit" value="search"/>
</form>
and on your php page have nothing but...
<?php var_dump($_REQUEST);?>
Tell me what you get.... I would chat with you but you don't have enough rep points to chat, so hence multiple edits.