Use a lint roller! Microfiber, even when it's put in the washer and dryer, doesn't always seem to get clean. The blanket will get rid of the dirt but not the pet hair. If you use a lint roller before you wash your blanket you should get most or all of the hair off the microfiber.
Try dampening your hands slightly and then brush the hair in one direction. You can also roll cellophane tape around your hand sticky side out and pick up the hair. Check out some of the new pet hair removal sponges, too.
Use a damp regular cellose sponse. Gently brush from cleaner areas toward to dirtier areas to collect clumps of furs. To get "missed" hairs use packing tape or de-linting paper.