You can play the hi-hats either with your heel up or down, depending on what you want to do. Whenever you play the hi-hats with your sticks, you want your heel down. To open the hi-hat, raise your toes slightly and release some of the pressure on the cymbals.
How much you lift your toes determines just how much your hi-hats will open and how long they will ring when you hit them. Most of the time you want a full swish sound. To create this sound, don’t open the cymbals too much. You have to experiment to find the swish sound that you like best.
At times, you may want to use your left foot to play the hi-hat while you’re playing the ride cymbal or another drum with your right foot. In this case playing with you heel up is the way to go. This technique is pretty much the same as the heel-up bass drum stroke. You can even do double strokes on the hi-hat pedal the same way.