In the main loop in index, to display the date like you are asking use:
<?php printf( _x( '%s ago', '%s = human-readable time difference', 'your-text-domain' ), human_time_diff( get_comment_time( 'U' ), current_time( 'timestamp' ) ) ); ?>
You can read more about it: https://codex.wordpress.org/Function_Reference/human_time_diff