Look at the markup for the callback function called by add_theme_page() or add_settings_page(), and use that markup to create a custom Page template.
For code that simply outputs content, this should be fairly straight-forward; for code that actually saves settings, you’re probably going to have to do more work in order to create front-end data submission. In such case, you might want to look at something like the P2 Theme, to see how it handles front-end post submissions.
However, before attempting something like this, be sure that you fully understand the security implications of taking such code/content out of the Admin area and putting it into the publicly accessible front-end.