Scientific American, in an article with lots of illustrations, examines the current thinking on how such monsters could fly:
One of the enduring mysteries of pterosaurs is how the largest members of this group became airborne. Giants such as Quetzalcoatlus, first discovered in Texas, and Hatzegopteryx, from modern-day Romania, stood as tall as a giraffe and had wingspans of more than 30 feet. These animals possessed jaws twice the length of those belonging to Tyrannosaurus rex. Their upper arms would have been nearly as large around as the torso of an average-sized adult human. They were true behemoths, attaining weights exceeding 650 pounds. For comparison, the largest bird to ever take to the air—Argentavis, living six million years ago in Argentina—most likely weighed less than 165 pounds.
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Some had skulls surpassing four times the length of their bodies.