I need the ability to add an image to a page, like a featured image. How can I do that, and how do I get the featured image to display in page.php? It can be a plugin if what I am asking can't be done within Wordpress itself out of the box.
Eek! A 33% acceptance rate isn't really going to do you any favours but lucky for you Wordpress' in-built post-thumbnail featured image functionality works for posts, custom post types and pages too.
Add the following line into your theme functions.php file:
add_theme_support( 'post-thumbnails', array( 'post', 'page' ) );
Then in your page.php file and I stress that this must be used within the page loop (not outside of it) the following function will show your featured image on a page if it has one assigned to it.
Adding a featured image to a page is the same process as adding one to a post. On the page editing screen you will see a metabox with a link that says, 'Set a featured image' click that and you're good to go. No plugins required.