We don't currently have a way to automatically post new K2 Items to a Facebook Page or your profile's news feed. That's something we're planning to implement alter this year.
Right now, and what we'd still recommend even if we have the auto-posting ability, is to make sure our Open Graph - K2 plugin is enabled. That will automatically set the title, description and image that will be used when the Item/Recipe is shared. Then, go to Facebook and simply paste the link to your page and add your own description. By doing that, you can use a targeted comment toward your Facebook audience, which is much better for user engagement than an automatic post.
I hope that helps explain, but if you have any questions, just let us know.
Thanks,
Alex