Start by looking for a particular practitioner, service or health condition in your area.
Booking a treatment usually involves getting undressed in a room with someone you have never met. It is worth five minutes of checking first, and almost nobody does it because nobody explains how.
The AHPRA public register is free and searchable by name. Acupuncturists must appear on it. Massage therapists and beauty therapists will not, because those professions are not registered that way — so an empty result means different things depending on who you searched for.
When they do appear, check that the registration is current and whether any conditions are attached.
Remedial massage therapists generally belong to an association that sets training standards and takes complaints. Ask which one, then look up the member directory yourself. Health fund rebates usually depend on that membership too, so it is a practical question as much as a safety one.
"Do you hold professional indemnity insurance, and where would a complaint go?" Two sentences, and the speed of the answer tells you most of what you want to know.
Before contacting anyone, read how they advertise. In Australia a registered health service may not publish testimonials about clinical care, may not promise results, and may not frighten people into booking.
A page of before-and-after claims, or "clients say it changed their life", is a signal about compliance, not about quality of treatment. And on the beauty side the line gets crossed constantly, so it is the place to look hardest.
Ask what the draping arrangements are, whether you can ask for pressure to change mid-treatment, and whether someone will be within call. Those are ordinary questions and should get ordinary answers.