Once you’ve added an image to the body of a post (below) simply copy and paste the image code into the “excerpt” panel when editing.
Then, when you show excerpts on your homepage, you’ll have a pre-defined image accompanying the excerpt text (it doesn’t need to be an image you show within the post, but in this case, you’ll see the above image replicated on the theme homepage).
You can even wrap the excerpt image code with a link to the full post, so visitors to your homepage can click on the image instead of only the “continue reading” link.