Regular grooming during the shedding season is also helpful.
Adhesives
Tape is a good method of removing hair from the surface of fleece. You can purchase a roller pre-wrapped with tape that is specifically designed for removing hair and debris from clothing. Another option is using painters tape to blot the fabric and remove hair. Experiment with different strength tapes to find the best strength for the fleece you own.
Vacuums
Use the tube extension on a vacuum to remove hair. Comb over the material several times until you can't remove any more. Vacuums work well on the surface, but they struggle to remove hair that is woven into the fibers. If the fleece has long-time exposure to dog hair, the vacuum may not work.
Rubber Gloves and Water
Rubber gloves are an effective tool for gathering the fur and removing it from the fleece. Wear a rubber glove and lay the fleece on a flat surface. Comb the glove across the surface to remove the hair. For stubborn spots, add a little water and continue combing with the glove.
Grooming Your Dog
Groom your dog on a regular basis to reduce the amount of hair on your blankets. Comb the dog with a high-quality brush weekly to capture loose hair before it hits your house. Also keep your fleece in an area where the dog has little opportunity to lay and rub on the material.