The most simple form of the featured images (post thumbnails) looks like this:
You need to have this piece of code in your functions.php file:
add_theme_support( 'post-thumbnails' );
Then in the index.php, or any other template file you want to show the post thumb or featured images, you would add this:
<?php the_post_thumbnail( 'thumbnail' ); ?>
The code above usually goes just after <?php the_title(); ?>
Once you’ve added those, you should see them on posts. To have them on posts and pages, use this in place of the first code for the functions.php file:
add_theme_support( 'post-thumbnails', array( 'post', 'page' ) );