Swipe a lint roller over the couch upholstery to remove loose fuzz. Tear off the sticky strip and use fresh roller strips as needed until most or all fuzz is removed.
Wrap a piece of masking tape around your hand, making sure the sticky side faces outward, and wipe over the couch upholstery. The sticky tape safely pulls off the fuzz without harming the couch.
Snip stuck-on fuzz off the couch carefully with a pair of scissors. This works well when you have matted patches of fuzz stuck to the upholstery but make sure to exercise caution so you do not cut the actual upholstery.