The manufacturer of Velcro suggests a stiff brush or another piece of the Velcro to remove accumulated hair, fuzz and lint from the hook side of Velcro fasteners. Regardless of which method is used, overzealous cleaning will damage the hooks and they won't be able to adhere to the loop side.
Adhesives, such as duct tape and lint rollers, can lift pieces of lint out if they are not too badly tangled in the hooks. Sliding a large blunt needle, metal toothpick or safety pin under the fibers, between the rows of hooks, can easily lift the fibers off. Carefully brushing the Velcro with a toothbrush, a stiff dish brush, a dolls hairbrush or a sturdy wire pet brush also works to remove fibers and small particles.
Another method is to use tweezers to pull the lint out, but this may damage the hooks. Bare fingers can remove bulky fibers, but will not remove materials that are tangled near the base of the hooks. Running the teeth of a Scotch tape dispenser carefully along the rows of hooks can lift some lint. However, the sharp edges of the plastic teeth could also damage the hooks.
For clothes that have hook-and-loop tabs sewn into them, keep the tabs closed as much as possible. This will help keep the hooks clean and will also keep the hooks from snagging other clothes. These cleaning methods also work on hook-and-loop hair rollers.