Unfortunately we can't do that if the person died a thousand years ago. There are several methods available to reconstruct a person that died in the recent past (within the last decades or centuries). More ancient or prehistoric populations are more difficult to reconstruct, because too much information is lacking. Our facial features and skull shape are not only genetically determined, but they're also influenced by our diet and lifestyle. Some "information", like hair texture, lip shape, nose shape (to some extent), skin/eye/hair color and wrinkles is very difficult if not downright impossible to determine without ancient DNA. I can list several Iron Age, Neolithic and Paleolithic specimens for which we have 5-10 facial reconstructions that look substantially different from one another. That said, ancient DNA has revealed some details that can't be deduced from the bones, like hair and skin color (google Cheddar man and compare his latest reconstruction to the ones we had before DNA analyses).