@ely https://www.repaircafe.org/en/ is a good place to start, but also, look and see if there's another RC nearby - most are happy to provide links, hints and mentoring to help set up another one. Each country has different legal requirements for doing this kind of stuff, so make sure you know what they are where you are. Having said that, it's usually pretty easy to set one up:
Find a group of like-minded people, form a working group, gather some tools and get repairing... you can run it almost however you like - formats vary from RC to RC. A common model is this:
1. Social media group to advertise and/or organise. Also posters in prominent places like supermarket bulletin boards, libraries, allied shops (zero waste ones are usually good) and venues.
2. Signage - pop up signs are good for use on the day to help people find you.
3. Admin desk with stationery - at least one person to handle disclaimer forms (essential), book items in and out, keep records and remind people to donate etc. Also to talk to potential recruits. Donation pots/bins.
4. Triage - someone to work out who the best repairer would be, and to spread workload across repairers.
5. Repairers with different skills. This will vary depending on the skills of who you recruit to help repair. You need to advertise the types of things you are able to tackle on your signage and social media posts. Typically this will include skills like: mechanical, electrical, electronic, woodwork, bikes, devices (laptops, computers, phones, tablets, etc.) textiles and jewelry. you probably won't be able to cover all these in the early days, but running the events is the best recruitment outreach.
6. Tools and materials. Most RCs keep a stock of adhesives, lubricants, random nuts, bolts, screws and nails etc. and some common and skill-appropriate tools like screwdrivers, pliers, bit sets, long power lead, circuit breaker, and so on. A lot of repairers like to bring their own specialist tools, but make sure they understand they take on the risk of using them.
7. A way to track repairs - we used to use a chalk board or dry-wipe board, but now we have paper forms. We (Telford RC, UK) were with an umbrella org called "Repair Cafe Wales/Repair and Share" for a while and they insisted on use of an online database. I say go low tech, low complexity for as long as possible as it keeps things easy and straight-forward.
8. On org structure, I'd recommend starting out as "just a bunch of people" with no official structure, and morph into whatever seems appropriate only when it becomes necessary. I'd personally avoid charity status if possible, and go with the lowest friction structure possible. You may need a committee, and you definitely need some (minimal) policies, and either a cash box or bank account.
All of the above are intended as general advice - pick and choose as you see fit, but I'd recommend going for the minimal options wherever possible, at least at first. Good luck, and if you have any specific questions, I'm happy to lend my opinion, and I'm sure many others on #RepariCafe will be too.