How to make your post to appear right here?
If you want to list your posts here, you should go to you theme's options (Appereance => Theme Options) and put the category's id. Please note that if the category doesn't consist any posts, you'll be still seeing sample posts.
How to assign a picture to a featured post?
Select a post & click edit through your admin panel. Scroll down to the section named "Custom fields" then create a field named "picture" and the value should contain a path where you stored a picture. You may also create a custom field named "url" just in case you want to link your post elsewhere.