This is a very "huge" question. I can say that we use an O/R Mapper and each "query" to the database needs an object called PersistenceBroker. This class is in charge of all the DB Stuff related to connecting, authenticating etc.
We've written a PersistenceBrokerFactory.GetCurrentBroker() which returns the "working" broker. If the DB suddenly fails (for whatever reason), the CONN object will "timeout()" after 30secs (or whatever you define). If that happens, we show the user that he/she is offline and display a reconnect button.
On the other hand, to provide a visual indication that the user has connectivity, we have a thread running in the background, that checks for Internet connectivity every 15 seconds. We do 1 ping to google.com. ;) If that fails, we assume Internet is somehow broken, and we update a status bar.
I could show you all that code for the network health monitor if you wanted. I took some bits from google and other I made myself :)