I would usually stand at the door and make a PA when the flight was going to be canceled due to a mechanical and explain the reason. I did this because I was there anyway talking with the mechanics and the agents really were not that up to speed on the precise reason and the technical explanation of why we could not go.
If we were going to be delayed for quite some time, I would also walk back to first class and explain to the customers that we were going to be late, what the reason was, and what I expected to be our new departure time. I would then make a PA to the aircraft. Simply customer service.