Whether you like it or not, you're responsible for cleaning up after your dog. Not only is the waste not a pretty sight (or smell), but it's also a breeder of germs and disease. Dog feces plays a significant role in water pollution, especially in cities, and the bacteria that makes its way into streams, lakes and the water table can make people sick.^[1] Here are some ways to minimize the unpleasantness of this task.

[edit] Steps

Take your dog for a walk. Bring a leash for them, and a plastic bag for yourself to hold. You could also tie the bag onto the leash.
Walk and enjoy the day out, but once the dog stops and smells the ground, be ready start removing the bag from your pocket, and start opening it.
Hold the leash with your one hand, as you maneuver the bag with the other. Or, if you are not alone, ask the other person to hold your dog's leash. Put your hand into the bag, grab the bottom of the bag with your fingers, and pick up the mess on the ground.
Use your other hand to pull the top of the bag over your fist, retaining the poop inside the bag.
Tie the bag tightly, and dispose of it in the nearest trash receptacle.
Continue to enjoy your walk with your dog.
Wash your hands thoroughly when you get home.

[edit] Tips

Always carry more than one bag.
Some pet supply stores have doggy bags that are scented. You may want to try some!
If you can't bring yourself to handle the poop, even through a plastic bag, purchase a commercially made "Pooper Scooper." These usually consist of a handle on one end of a long arm, with a double-sided shovel on the other end.
When picking up with a plastic bag: On Concrete, gingerly lift the poo directly up from the surface to leave as little behind as possible. On grass, make a claw like circle with your fingers-get as far under the poo as possible, then lift.
Plastic grocery bags work great for picking up dog poop. These bags do sometimes have a tear or two, so it helps to use two bags - one inside the other. This way the odds are extremely small that there will be two holes in the same location and you are almost guaranteed not to get poop on your hands. Using two bags also has an insulating affect so that you don't feel the heat from the poop as much. And it also works better in keeping the smell down.
Holding your breath until you've picked up the poop and tied a knot in the bag(s) helps a lot.
You can make your pet's poops more tolerable to yourself by better choices of pet food- too much canned meat makes the poops more malodorous and looser, while better dry foods such as Innova will make the poops smaller, drier, and MUCH less smelly; feeding only dry foods also helps keep teeth cleaner and gums in MUCH better health, which helps to extend life span.
Assert yourself when you see an irresponsible or unprepared pet owner who fails to pick up their pet's poop by offering them one of your own extra bags, and if they don't take the hint then tell them bluntly that unless everybody does their share to avoid making public nuisances of their pets, then all pet owners alike will suffer from the inevitable public outrage and resulting pet limitations.

[edit] Warnings

Leaving the poop on the street, or in the park is against the law in most states. It can carry a heavy fine. So enjoy your dog, but at the same time keep the streets clean. Pick up after them!
Do not touch the feces with your hands, especially if you have an open cut. Always wash your hand after a dog walk when you have picked up poop.