Here are ten exercises that you can use to help develop your foot pedal independence for the hi-hat. All of the exercises except for the last two are in 4/4 time. Exercises 9 and 10 are in 6/4 time. During the course of the ten exercises, you will use the hi-hat in a variety of different ways, sometimes on the two and four beats, sometimes on all beats, sometimes on every other eighth note, etc.
This exercise can be difficult at first because developing independence is one of the hardest things about becoming a drummer. As with all things with drumming, and indeed with music in general, you'll need to start off as slow as possible. As you gain the skill to play the patterns evenly and consistently you can speed up the patterns. Also, as always, practice with a metronome will provide the most beneficial practice.
Learn how to play accent notes in the next drum lesson.