If you want the activity stream as your front page – go to wp-admin … settings … reading … front page displays
If you just want a small area to show updates, try a widgetised theme, and add the sitewide activity widget
If you want something more bespoke, i.e. just status updates… you will have to write your own custom activity loop – check docs on this site for information on this. Make sure you do this in a new or child theme.
Here’s a tutorial showing how to changed the default activity tab: http://shabushabu.eu/reordering-buddypress-group-tabs/
