I want it to be possible for the users to edit and delete their own posts, not only through the admin panel as it is by default. I’ve look around on the net but haven’t found any information about it.
How can this be done?
Edit / delete custom post types through web page (not admin)
Take a look at http://wordpress.org/extend/plugins/front-end-editor/
If you assign users the Contributor role, they’ll be able edit their own posts from the frontend. You could use a basic redirect to prevent Contributors from being shown the admin panel on login… look around StackExchange/Google for several solutions to this.
For another solution, which will give you more control over the process (including adding/editing/deleting posts), check out the tutorial at http://wp.tutsplus.com/series/posting-via-the-front-end/