How to determine high availability configuration is working correctly

Question

I am in the process of setting up always on high availability clusters for the first time. Can anyone explain to me from the networking perspective after configuring the group and testing to make sure it is functioning properly, how does SQL know when to fail over, and how would my application connecting to the SQL server know where it is pointing?

So for example I have an application foo connecting to a named instance DB01.FOO. When foo fails and is rolled over to DB02.FOO, how would my application know it should be talking to DB02.FOO?

DB02.FOO is in the same domain but a different server. I am just trying to wrap my head around all aspects of this before attempting it. If there are any links someone would recommend that would be awesome as well.