How to keep form values after post

you can save them into a $_SESSION variable and then when the user calls that page again populate all the inputs with their respective session variables.

If you are looking to just repopulate the fields with the values that were posted in them, then just echo the post value back into the field, like so:

<input type="text" name="myField1" value="<?php echo isset($_POST['myField1']) ? $_POST['myField1'] : '' ?>" />