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/