Automatic excerpts

general:

locate the template for the home page – often index.php – if not see http://codex.wordpress.org/Template_Hierarchy

find the_content() (possibly with some parameters in the brackets) and change that to the_excerpt() – http://codex.wordpress.org/Function_Reference/the_excerpt

specific for Twenty Eleven:

index.php points to the template part content.php;
in content.php edit this line:

<?php if ( is_search() ) : // Only display Excerpts for Search ?>

change it to:

<?php if ( is_search() || is_home() ) : // Only display Excerpts for Search and posts page ?>

http://codex.wordpress.org/Conditional_Tags