Giants generally sleep motionless. They can resemble hills which many people walk across and never know. They can be quite violent if bothered. When a giant takes on a new territory it will create a forest fire to stake it's claim. A giant's territory is usually marked by lakes in the shape of footprints, trees knocked over without cause, hills made of poo, boulders in odd places.
* photo courtesy of Arthur Spiderwick's Field Guide