exAC is correct. It is easy to tell if the approach is flown by the autopilot. If the aircraft comes down final approach with no noticeable path correction, the approach is flown by the autopilot. (ie the wing stays steady on the horizon, no rolling)

Also, autoland touchdowns are usually "firm". It lands firm by design to ensure positive weight on wheels. This ensures that the aircraft can have positive directional control/positive braking action once on the ground. Recall that there was an A320 accident in which the aircraft ran off the end of the runway in Warsaw. The aircraft was piloted by a LH check pilot, and the touchdown was so soft that the computers did not realize the aircraft has touched down (much simplified version). No braking and no reverse caused the aircraft to go off the end of the runway. Autopilots land firm to avoid situations like this.

Most landings are manually flown; pilots usually only use autoland for currency requirements. Why? If you drive a stick, how do you feel when you have to drive a rental automatic?

So to answer Altaflyer's question, yes, A319/320/321s have autoland, and no, autoland is not routinely used.