To make a recipe private/public, visit the recipe page and select the three dots located at the top of the screen > "More Options..." > "Edit Recipe." From here, you can make your recipe public by tapping on the "Make public" link. Once you're finished, scroll to the bottom of the screen and hit the "Final Check and Submit >>" button.
Please also note that making a recipe PUBLIC, you cannot later change it back to private state.
By default, all clipped recipes are made public -- this is because more than one user can import the same recipe. Conversely, RecipeScans are uploaded as private. Users can set the status of a typed in recipe when adding the recipe -- simply check the "Public" or the "Private" box.