Enroll in classes to study Sufi culture. Many colleges and universities offer studies in Islamic faith, including Sufism. Certain universities may offer classes in Sufi music. Learning the basics of Sufi thought and practices will enhance your appreciation of the music, art, and poetry of the Sufi as well as adding to your knowledge of world culture.
Attend Sufi music workshops, and, if possible, prayer meetings. These workshops may be available right in your city, or you may have to travel depending on where you live. The workshops bring Islamic people together to study and discuss the Sufi way. They often have music and poetry that you can be a part of.
Download Sufi music from the Internet. Prayer manuals can be helpful as well. These are available on a few different websites including TheSufi.com and National Geographic World Music. Listening to some Sufi songs is the best way to get a feel for what this kind of music offers.