If you've been getting ready since a hurricane watch was issued, you should be prepared to take off the minute you get evacuation orders. The longer you wait, the bigger your chances of getting stuck in a massive traffic jam. Try to consolidate everything as much as possible when you're packing -- the fewer cars on the road, the better, and you'll also want everyone in the same place. No need to pack up everything you own; just take the necessities.
If you have time, disconnect appliances (so there's less risk of electrical shock when power is restored) and turn off the gas, electricity and water before you leave. Make sure you have all important papers and documents with you -- ID, insurance policies, wills -- as well as medications.
You're going to hit more congestion the farther you drive, so try to pick the closest possible evacuation destination. The best-case scenario would probably be a friend or relative who lives in your area but doesn't have to evacuate. Don't be tempted to avoid traffic by getting fancy with your route -- follow the official evacuation routes.
If you have room in the car, bring your disaster supply kit. If you do end up staying in a shelter, you never know what kinds of conditions you might encounter. A shelter should be your last resort, especially if you have pets -- many don't accept animals.
When the storm has subsided, don't rush to return home. Wait for instructions.