How did archeaologists know where the ship Andrea Doria wasn located?

Answer 1

That is easy - the position was logged by the crew of the Stockholm, which, despite the severe damage to the bow, could return to New York by her own power. The Andrea Doria did not sink until the next day, and the sinking was witnessed by many ships that had assisted in the rescue, and so everybody knew exactly where she went down. Most of the wreck have collapsed into itself after more than 50 years on the seabed, but most of her fittings, china, safes, etc have long since been removed.