The 2 main advantage of showing excerpts on your blog homepage are

• Holding your visitor a bit longer on your blog.
• To remove duplicate content.

The code for applying the excerpt rule is quite simple but I would suggest you all to save a copy of your website theme files before you make any changes if them.

• Open  your index.php file (some cases it will be home.php) using your wordpress editor from the dashboard.
• Search for this php code the_content( )
• Delete all of that and replace it with

<?php the_excerpt(); ?>

<a href=”<?php the_permalink(); ?>” title=”Read the rest of <?php the_title(); ?>” class=”more-link”>Read More »</a>

Now you are done. Save the file and check your home page.

Where other places can I show the excerpts?
The other 2 places where I would suggest using the excerpt code is categories.php and archives.php.
Usually your wordpress theme settings would be such that it will display whole blog posts in those blog pages.