A 'field' just refers to an input in the form. So it might be a textbox or a select menu or a checkbox. All are seen in PHP in the $_POST array (or $_GET if you use that method-- not so common), and there's no difference except what types of data (such as true/false, 1/0, text, a preset list of terms, etc.). So this means you should rename your textbox input name="myfield" (for example).
As for a redirect, you can find lots of information about that by searching. The basic answer is the following: since it is done through a header, it must be sent before any HTML output to the browser, including even line breaks. This means you'll need to pre-process the form data (at least the 'myfield' value to see if it is valid) and if you need to redirect do it early, so check if the value is INVALID then redirect if that's the case.
http://php.net/manual/en/function.header.php
PHP Code:
<?php header('Location: http://www.example.com/'); ?>
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