"The files"? It should be one file only, ending with .upd.
The put in the card and turn it on, is right. When booting the Elite checks the card and should do the update automatically. On my Elite 5, I had to do a hard reset to get it to do the update so you might want to try that. Do the hard reset, turn off, Insert card and start the unit. If you have any waypoints or routes on the unit that you want to save, back them up to your memorycard before the hard reset, since the reset will delete all of them.