Remove the lint from the lint trap in your dryer so that the fuzz from the fleece and other items has somewhere to cling other than on the fleece itself.
Turn the fleece inside out before putting it in the dryer. This will help preserve its life.
Avoid adding other items in the dryer that let off a lot of lint and fuzz, such as towels and blankets. Also, do not use a dryer sheet, which can damage the integrity of the fleece, such as its ability to repel water.
Add two tennis balls to the dryer if the fleece is a large item, such as a blanket. This will help prevent the fleece from balling up and will help it maintain its fluff. Tennis balls also help reduce static cling, which reduces the likelihood of fuzz and lint sticking to the fleece.
Dry the fleece on the lowest setting for about 15 minutes. It should not need long to dry.