'Out of the box' its a manual process, if you have server names in the connect string for your app pointing at serverA then it will need to be manually changed to ServerB (My vote is App support should be responsible for this, but it will vary between companies).

One (of many i'm sure) way to potentially make this simplier could be to use a DNS alias for the application connect string, so when you fail over, change the DNS entry to point at ServerB...although would still be a manual process, its only a single change to make.

Rod