How do I show a preview of a post

I’ve seen on other websites especially those using the Lightword theme that they display a preview of the post on the index page. When the reader clicks the header or a read more link they are then taken to the real post.
How do you do that?

Its annoying because if I make a really big post the whole post appears on the main page and from here it is not obvious how to comment on the post.

I want my readers to get to the end of a post and see the related articles and comments section rather then another big post following directly after it.