BuddyPress 1.0.2 is out now.
As with previous upgrades, the best way to get the latest is through the plugin browser in your WordPress installation (de-activate BuddyPress before auto-upgrading).
If you are using a language file with your installation you will need to re-download this after your upgrade. From version 1.1 onwards, we’ll bundle as many language files as possible to make the upgrade process smoother for non-english installations.
If you would like to upgrade manually you can download the latest then simply overwrite your existing plugin files (and themes if you are using the defaults). Please make sure you backup everything first.
This is not a critical upgrade, so it is not essential that you install this update. It does however fix a number of bugs that will improve your BuddyPress experience. For a full list of fixes, please see the updated release history.
Update: Please make sure you de-activate any 3rd party BuddyPress plugins before deactivating BuddyPress and running the auto-update.