No, it's not an app. It's fairly invisible to the user, except that you should have more internal memory available because most of the apps are actually on your ext partition. Note that if you go into menu->applications->manage apps these will appear to the phone to be in internal memory, not on SD.
Run Titanium Backup and look at the statistics at the bottom of the overview page: that will include the side of your "SD card (A2SD)" partition and how much of that is used. If it's being used, then your A2SD is working. There are other apps, such as "quick system info", which can show you this as well.
Edit: P.S. Yes, it should be automatic.