This is not really hard with K2...

- First of all, when a user signs up to your site, automatically assign them to a K2 user group. See K2's Settings for that.
- The K2 User Group that all users are assigned to can utilize special content submission permissions. E.g. you can allow users to post content to specific (or all) categories, allow self-publising or not and more.
- Make sure you create a category that is meant for user submissions only or allow users to select an actual category (provided you've assigned that in the related K2 User Group).
- Finally publish the K2 User module so any user can see the content submission links.

I would recommend signing up in getk2.org to see how it's done there.