In terms of deciding if you want to Be A Quaker more generally, the best first step is to check out a Meeting for Worship and see if you get anything out of it.
If you're in the UK, you can find your nearest Meeting on the Quakers in Britain website, including contact details and where and when they meet.
Find a Quaker Meeting near you
Depending on how many Quakers there are in your region, your nearest Meeting might be quite far away and/or might not have a permanent home (some smaller Meetings are in people's homes, or at odd times because they're using a heavily-booked space).
If that's the case, or you're not able to find one you could get to at all, it might be worth emailing your nearest one to say hey, I'm interested in coming to a meeting but I live all the way over here. @mangled-by-disuse might have better insight on this, cause their previous home Meeting was in the big-geographic-area-small-membership kind of situation, whereas I'm pretty spoiled tbh.
On the other end of the spectrum, in bigger cities or more historically Quaker areas like Yorkshire and the West Midlands, you might have several to choose from. In that case, my suggestion would be to go to all of them and see what vibes best for you!
The Quaker approach, as a space that's meant to be welcoming but not evangelical, generally means you're very welcome to dip in without making any kind of commitment. If there isn't a local Meeting you can join, all Meetings are open to visitors - I often look up local meetings if I'm traveling for other reasons over a weekend, and that can be a nice low-impact way to test the waters.
(having said this. Quakers are human people (and often old middle class white people), and sometimes you'll go to a Meeting and it will be lovely, and sometimes you'll go and someone will be rude, or nobody talks to you, or you just won't feel welcome. This sucks. I encourage you to try another Meeting, or another time, before assuming that means Quakerism isn't for you, but also it is really hard. I had a really negative experience trying to join my local Meeting in like 2015, and it took me almost a decade and a different Meeting to try again - if I didn't already have plenty of positive experience with Quakers before that I don't think I would have ever given it another shot, and that would have been a shame)
If you do find a Meeting that's a good experience for you, there isn't really a formal conversion or joining process. You can just go if and when you want to go, and you are fine to go for a bit, go away, and come back another time.
If you're going to the same meeting moderately regularly, it's nice to volunteer to help out as, when and how it works for you (eg with welcoming, refreshments, setting up and packing down, helping with childcare during meetings, etc). Most meetings have rotas or ask for volunteers for things during the notices.
Formally Becoming Part Of Quakers (applying to be a Member of the Religious Society of Friends) is very optional, and you're expected to do it at your own pace - in some cases, people are like THIS IS WHERE I WANT TO BE FOREVER and apply within a few months, but more usually you'd attend Meetings for years or decades before becoming a Member, it's up to you.
If you're not a Member but you are part of your local Meeting, you're an Attender, and that is already solidly Quaker. Many Quakers aren't Members yet but they've been attending the same Meeting for years. I've been attending Quaker Meetings on and off my whole life, and considered myself religiously a Quaker since at least 2015, but I too am not currently a Member (although I'm planning to apply this year).
The thing about Quakerism is it's a religion for people looking to direct their own spiritual journey rather than be directed, and as such it's not just normal but encouraged to turn up, try it out, see if it's for you and vibe out what it looks like for you.
um. The other thing about Quakerism is it's extremely obtuse and has all the micro-committees and jargon of any long-standing non-hierarchical organisation. and so you can try to do research beforehand but other than checking out local meetings you'll get loads of great history of Quakers but nobody will write an easy-read article explaining what an Elder is for or what Membership actually means. so you can read the manual (that's Quaker Faith & Practise, which is a periodically-updated collection of quotes and specific guidances from the last 400 years, organised by theme)
but also. you can just ask. if you go to meetings and everyone is talking about idk holding someone in the Light during this difficult discernment, it can feel like you're asking a stupid question if you're like hey. What does that mean. But honestly man half the people there are also trying to figure it out and the other half don't mind explaining. I grew up in Quakers and I went to Meeting most Sundays as a kid and I went to Quaker summer camp and I've been going to my current Meeting for like a year. and I'm not gonna lie I still don't understand half of the language.
but despite the trappings it's not about administration or non-hierarchical decision making techniques or volunteer roles it is. about whether it speaks to you and fills a spiritual or social hole for you.
for me I am fucking Struggling constantly with my own weakness in the face of the enormous injustice of the world and when I go to Meeting I feel held in something that welcomes me as a flawed person. and I have never felt God when someone's telling me how to look for it or to bow down to it but I'm not going to lie I have seen God in Meeting for Worship and although I don't have deep spiritual revelations every time, that's not the point - the point is that there's space to hold them if they come. and that we're all in that open place as a group. there's a texture to a room full of people all listening. it is something I genuinely need.
(you don't need to be looking for God though. a lot of my Quaker friends are atheists or entirely uninterested in the question of the divine, and they get a lot from Meeting as a space to breathe, or to meditate, or to listen to their own thoughts, or to connect with other people, or as a political coalition, or any number of other things)