
Prevent hairs from entering your vehicle in the first place with a thorough brushing before the ride. Whatever area your pet rides in should have a towel or a pet cover placed over it. Keeping your pet inside a carrier will do a lot to contain any hairs or dirt and is also safer for your little friend.
If you notice some hairs that have managed to get caught in the weave of your upholstery, you can put on a pair of rubber gloves and spray down the area with water, rubbing vigorously in one direction to collect the hairs into clumps that you can easily pick up and dispose.