Know the story of the ballet. Most ballet choreography references a story or tale. Even ballet pieces that seem abstract have a concept behind them the choreographer is exploring. Interview the choreographer if possible. Watch rehearsals and preliminary performances to learn entrances and exits and the pattern of the choreography. Write down shot ideas that will clarify the key moments and the relationships of the characters onstage.
Establish a point of view. You won't be able to follow every dancer on the stage. In general, follow the lead dancers. They are most likely to establish the conflict, development and resolution of the piece. Break away from their movements occasionally to catch the supporting dancers, but always bring your audience back to the leads. If it is a solo piece, film the dancer from many interesting angles, but be sure you capture all the major moves that develop the piece. If possible, use more than one camera to ensure you get all the shots you need.
Mix close-ups and long shots. Give your audience variety by changing the distance you film from. Faces are the most expressive part of the body, but dance films must have a preponderance of shots that include the entire body, especially the feet. Include wide-angle shots to capture the panorama of a company of dancers filling a space with movement. Variety is key. Mix close-ups, full-length body shots and wide-angle shots and you'll have a more interesting film.
Capture the music using separate microphones. Don't rely on camera microphones. If the music used in the performance is recorded, use the orginal recording in the film. If the music is live, place microphones around the orchestra and record the music on professional equipment. You can easily add the music soundtrack to your film after editing.