For now, the only application supported by Google Calendar is Apple's iCal. "With CalDAV support in Google Calendar, you'll be able to view and edit your Google Calendar events directly in iCal. Any changes you make in iCal will automatically appear in Google Calendar the next time you sign in (and vice versa). If you use iCal while offline, changes you make will be saved and updated in Google Calendar when you get back online."
Rick Vugteveen tested the new feature and found that the 2 way synchronization works well, but there are some problems. "The largest issue that I had is that I needed to create a new CalDav server account for every calendar in Google Calendar. Not only did this make further setup cumbersome, it degraded the iCal UI as a 1-1 relationship between each folder (server) and calendar is created. Normal re-ordering and organization of calendars does not work with this setup so be careful with the order you enter your calendars. This multiple server setup also removed the ability to move events between different calendars within iCal."
This page provides instructions for adding your calendars in iCal and you should also read the known issues.
Google Calendar also provides basic applications for synchronizing data with Blackberry devices and Outlook, but there are many third-party applications that use Google's API to add more advanced functionality: Spanning Sync (iCal - $25/year), BusySync (iCal - $25), Calgoo (iCal/Outlook - free), SyncMyCal (Outlook - $25), gSyncit (Outlook - $10), GCALDaemon (cross-platform/open source), Plaxo (cross-platform/free), GCalSync (Java mobile app - open source), GooSync (SyncML service/mobile app - £20/year), GMobileSync (Windows Mobile - open source), OggSync (Windows Mobile/Outlook - $30/year).