How to make a custom post/page template?

Hey

When making a post or page, you have the choice to assign it a custom template. What I want to know is how to make such a template? I’ve tried just adding a php file to the theme directory, but it doesn’t show up in the drop down menu on the Create New/Edit Post/Page pages.

So how can I achieve this? Any special code I need to include for WordPress to recognize it as a template file?