It's tricky because psychotherapy isn't a protection profession, so all the "governing" bodies are effectively membership groups - psychotherapists don't need to join and membership/accreditation doesn't mean a huge amount in terms of knowledge and experience. Qualifications range from a 2 year Diploma course to Master's level training and courses all look quite different.
I'd look firstly at their qualifications, they should tell you the level they have studied to, Post Grad Diploma or Masters level is what I'd look for. Then look at how long it's been since they qualified and if they tell you where they've worked, eg private practice, within an organisation etc. Look at what they say they want to offer, eg some are very relationship based, some will actively focus on change - what form of therapy to they offer, CBT is good for looking at symptomatic stuff that gets in the way of day to day living (eg with anxiety or depression), psychodynamic and person centred tend to be more relationship based therapies where you have space to talk about underlying issues etc.
Speak to them before you arrange to meet them. Ask about their experience, do they have experience in working with the things you need to talk about, what made them decide to become a therapist, have their had their own long term therapy (it's ok to ask, any therapist worth their salt should have had a decent amount of therapy themselves, it's an essential part of training). Do they have clinical supervision, how often - monthly is an absolute minimum. Ask them how they work, and why they think that might be helpful to you.
At the end of the day, the relationship you have with them is key, if you don't click when you speak to them don't take it any further - it's a perfectly good reason to not book a therapist or to leave therapy. Finally, avoid those who tick every box in the "issues" list, or every box in the "types of therapy" box, no-one can work with everyone and too many modalities suggest they know a lot about everything but not much of anything.
I'm a therapist and that's how I decide when I'm looking for a personal therapist.