How did they get the walls and roofs up there?

In the same way that builders do now and have done throughout history: with cranes and scaffolding. Despite a pop-culture idea that everybody in the medieval period was an uneducated idiot living in a squalid hovel, medieval Europe was capable of highly advanced construction techniques far beyond the scope of the Classical world, it was just a matter of mustering the logistical - rather than technological - means to do so.

Medieval scaffolding was very similar to today's, albeit wooden rather than metal, so as you'd imagine we have little by way of surviving examples, although we do have illustrations. Cranes could be simple pulleys, but medieval engineers were also fond of rotary-wheel cranes powered by treadmills or by animals. These can be seen in many contemporary illustrations such this one from William of Tyre's Histoire d'Outremer. You can actually visit a surviving 14th century example at Chesterfield Museum in Derbyshire.