You can go this way.
A submission goes to the script, say, 'post.php'.
This script processes the information, does all you need, and then redirects a user to another page, that shows him the output. Then refreshing this page won't submit anything.
To be more accurate, you may completely remove post.php from history list. The only way i know is to use the javascript redirect
'window.location.replace()', but it isn't much reliable 'cause JS may be off.