Qualifications
In this job, what you do can really determine the best path to get there. For example, massage therapy requires licenses and special certifications. Aromatherapy, on the other hand, isn't recognized by any official regulatory agencies. It pretty much requires nothing. That said, we doubt people are going to pay you much to hold a mango under their nose and say, "Uh, did that make your leg stop hurting?"
You still need to know what you're doing. Mind boggling, we know. Having specific training is key regardless of whether or not your craft can be "officially" studied and qualified.
This can be accomplished as easily as finding a college that offers a degree in complementary and alternative health or holistic studies.
Once that's in hand, research what you want to do, then seek out training and certification courses for the skill you're hoping to master. Even if it's not sponsored by the state in any capacity, such programs can be helpful for learning the ins and outs of everything from Asian body therapy to therapeutic massage.
Alternatively, you could also go the more traditional route and find someone who'll take you on as their assistant or apprentice. Holistic health practitioners are typically self-employed, so in lieu of trying to impress an employer, the most important thing is to be personable, market yourself, and know what you're doing (source).