Start off by walking on your toes. You basically have to learn to walk "backwards": walking barefoot or in flats requires putting your heel down first and rolling the foot forward to your toes, while in heels you either lead with the ball of your foot (the easiest way to start practicing) or plant your whole foot down at once.
Start by walking on your toes (not really your "toes", but the ball of the foot) because it's a sensation you're more likely to be familiar with. Once your comfortable walking in the shoes without letting the pointy little heel bear any weight, you can start rolling back onto it a little to get the feel. Get the rolling motion/time smaller and smaller until you're stepping your whole foot down at once.
As pointed out, walking like this uses different muscles than normal walking so you may be a little sore after the first few times, but it gets better with practice. Planting the whole foot down is better than constant ball-heel ball-heel stepping because it's faster, but you really have to be careful as the more weight you allow to be put on the heel, the more likely you are to turn your ankle.