It's relatively easy and well documented to output a featured image, but getting the caption is a little trickier. Here's the code I use:

$post_thumbnail_caption = get_post( get_post_thumbnail_id() )->post_excerpt;

if ( ! empty( $post_thumbnail_caption ) ) {
echo '<p class="featured-image-caption">' . esc_html( $post_thumbnail_caption ) . '</p>';

Note: If you are expecting to output HTML inside captions, use wp_kses_post() in place of esc_html(). While not as performant, it allows the same tags that are allowed inside post content, such as links, italics, bolding, etc.

Last Updated: 2/3/2016