Purchase Irish step dancing shoes from a vendor that carries the different kinds that are needed. As a beginner, you'll want to purchase the harder-soled beginner jig shoes. As you progress and get better, you can try a flex-soled shoes that are easier for more complex moves. You'll notice that those dancing Riverdance have metal plates on their shoes; this is for a louder sound, but is not necessary to learn to dance.
Enroll in a class with an Irish step dancing company. There are different types of step dancing, so make sure that you enroll in a jig or step dancing class. If you are an adult, you'll need to find a studio that offers classes for adults, as most cater to children only.
Attend class regularly and work on your step dancing. You may find that at first, it is a complicated process. However, once you become acquainted with the different moves and steps, it will become easier for you as time goes on.
Practice your dance steps away from class as well. Ask your teacher for a recording of the music from your class, or just play your Riverdance soundtrack as you practice all of the new steps that you've learned.
Attend a feiseanna, which is a traditional competition and recital where regional Irish dancers can come to show off their skills. Perform your routine with your dance class in front of those who attend the feiseanna, Irish step dance enthusiasts and other dancers. Once you've competed, you are officially an Irish step dancer.
Watch a recording of Riverdance to learn and mimic the steps that the dancers perform. With a new knowledge of Irish step dancing and the ability to do the moves, you should find it no problem to dance along with your favorite Riverdance characters.