That is usually dependent upon the theme that you are using. But you can also manually set each blog post to only show so much with the <!-- more --> tag that you insert in to each post.
If you’re wanting to update the theme template file, you’d replace the_content() function call with the_excerpt() function call (see the Codex for details on how to use) in the template file that is being loaded on your home page which depends upon the theme. Could be front-page.php or archive.php or index.php in your selected theme’s directory.