Rule #1
De-hair the fabric as much as possible before washing!!
Rule #2
No synthetic fabrics.
Rule #3
Wash anything with pet hair on it seperate from EVERYTHING else.
I have a cat that sleeps on the bed. Before washing the comforter I vacuum the comfortor. By "vacuum" I mean I lift the vacuum up on the bed and go over the comforter just like vacuuming the floor. If I don't do that there is no amount of washing that will get rid of the hair. Also, the dryer won't blow it out the vent, at least not all of it. The coarser hair, maybe. Downy undercoat hair? No way.
Synthetic fabrics create static in the dryer. That draws hair to to fabric like a fat kid to donuts. Dryer sheets help, but only to a point. You can also try the multiple rinse/dry method. Dry the fabric on low heat until it's barely damp, then run it through another rinse cycle and dry again. Keeping the fabric damp will keep static electricity at bay. Also, put fewer things in the dryer. The more things tumble around as they dry, meaning surfaces rubbing together as things tumble, the better the chance of the hair being rubbed off and removed by the lint screen.
About the only sure-fire way to end up with no hair on your clothes after the wash is to make sure there's no hair on them when they go in. Vacuum, lint roller, whatever. It's a pain in the rear but that's the price of living with pets.
Brad