It's indeed done by mod_rewrite, or with multiviews. But i prefer mod_rewrite.
First: you create a .htaccessfile with these contents:
RewriteEngine On
RewriteRule ^posts/([0-9])/(edit|delete)$ /index.php?page=posts&postId=$1&action=$2
Obvious, mod_rewrite must be enabled by your hostingprovider ;)