Music is an essential part of the waltz, because a waltz can only be done in three-quarter time. This means there are three beats in a measure of music, mirroring the three-count structure of waltz steps. Waltz music has a strong downbeat on one, and music is often "felt" in one beat, rather than in three. For this reason, slower music is preferable when learning the waltz, because beginners need to learn to divide the beat into three to match the count of the steps.
The waltz is a smooth dance characterized by a rise and fall motion created as dancers lift onto their toes during the first beat and settle back onto their whole foot during the third beat. The modern version of the waltz is slower than its 19th-century predecessor, and almost twice as slow as its contemporary, the Viennese waltz. The poised and elegant nature of the waltz makes it hard to remember that when the dance first debuted in England and America it was considered inappropriate and scandalous.
The basic waltz step is the box, named for the box-like shape the feet trace on the floor. For the man: Step forward with the left foot, then forward and to the right with the right foot (this step should bring the right foot parallel with but not directly next to left). Then close by bringing the left foot over to the right. This is the step-step-close three-count step of the waltz. Complete the box by stepping back with the right foot, back and left with the left foot, and then closing the right foot to the left foot. The woman's part is the same steps, simply in the opposite directions. (Hint: The steps are exactly the same, the woman just starts with the second half of the box, stepping back with her right foot).
Once the basic box is mastered, the dancer must learn to rotate it. This is fairly easy--all that changes is the direction of the first beat. For a left (counter-clockwise) box turn, instead of stepping to the front, step to the left. Bring the right foot parallel with the left foot, which will swing the rest of the body to face left. From this position simply close with the left foot, just as with a stationary box step. The next step back with the right foot should be to the right, bring the left foot parallel, and close. One complete box will be half a rotation--two boxes completes the rotation.