Enable the path module on the modules page at Administer > Modules (Administer > Site building > Modules in Drupal 6). When users with the right permissions create or edit posts, they'll see a field for "URL path settings." That's where they can enter an alias of their choice.
On the URL aliases page, at Administer > Configuration > Search and metadata > URL aliases in Drupal 7 (Administer > Site building > URL aliases in Drupal 6), you'll see a list of all the URL aliases on your site. There you can edit them, and add new ones. You can assign more than one alias to a page (just use the add alias tab again for each new alias).
On the permissions page at Administer > People > Permissions (tab) in Drupal 7 (Administer > User management > Permissionsl in Drupal 6), you can decide who can create aliases and who can administer the list of them.