They study the image in the shroud, ways the image may have been formed, fabric related issues, pollen counts, all sorts of things related to the shroud, like the mechanics of crucifixion and scourging in the Roman era; some try to discover the history of the cloth before it turned up in Italy, and so on.
Some of them believe it's a miraculous image, some of them believe it's a medieval image, made by human hands, some of them are probably somewhere in the middle.