Riding two-up can be one of motorcycling's great experiences, especially if you and your passenger of choice enjoy a trip across a few state lines instead of simply across town.
But riding with a passenger is Serious Business--for all the obvious reasons. It isn't just your butt you're responsible for, remember. And there's more to it than simply being extra careful out there. Making sure your passenger is "on board" psychologically is every bit as vital as teaching him or her how to hold on correctly.
It always helps to be sure the person you're about to whisk toward the horizon is willing and ready--really ready--to be whisked. Few things are worse than an uncomfortable or petrified passenger hanging on to the back of your bike. Determine first if they've even been on a bike before. If not, spend a few minutes with them prior to start-up and give them the scoop on how to sit and hold on securely (and in a manner you're comfortable with). Tell them to not lean off the side of the bike, but to remain in line with the bike as it leans. If the bike you're riding doesn't have grab rails or a backrest/sissy-bar, have them hold onto your waist and not your upper body; doing the latter will be far less secure for them.
(A "Buddy Belt" type of device that straps on the rider's waist and offers passengers specially designed grab handles is perfect for two-up riding, especially when the passenger is a rookie.)
Then work out a basic plan for on-bike communication. It's easy enough to speak with a passenger during around town riding, but it's tougher on the freeway, so work out a few basic hand signals; a pinch here or a tug there is usually enough to let the rider know the passenger's wishes. Make sure they've dressed appropriately. Then develop some simple rules: not jumping off/on the bike until the rider says so, don't put your feet down while moving, etc. The toughest job, of course, is the rider's.
A passenger's weight can radically change a bike's handling behavior and stopping distance, so be sure you're familiar with the concept before you put someone on the back seat. Be smooth with throttle and brake inputs, have an eagle's eye for errant cars and cell-phone toting drivers and practice "the scan."
Above all, strive to give your passenger a good two-up experience; plenty of backseaters become riders themselves, and nothing kills the desire to ride more quickly than a bad backseat experience.