What tips do you have for hiring a League of Legends coach?

What you expect vs What you can afford.

For your expectation, it's the best if you know what you need. Coaching style, champion pool, aspects you want to improve on, roles, are all great reference. It would be even more important if you are Master-GM+ . If you are an otp then looking for another otp, or at least a coach who is maining your role would be the optimal call.

For your budget, price is not the only factor here. Mental, time, talent are also things to consider. A player need games to improve, even kkOma from T1 couldn't do much if a player can only play 2 hours a week. So make sure you can afford not only to get the coaching session, but also the time and mentality to practice and put in the work after the session (or between the sessions if it's a long term plan)

Put these two things together. Think about your desire, then consider if the services from the coach is worth it. Looking at a coach's review to check more about the coach is also a great reference.

First of all I think you should look to fix the matter of the language: if you're not a native English speaker (I am not one either), look for a coach that can talk your own language, as well as English. You might find a great coach but if you can't understand each other, the experience will be rough.

Second, look for someone that specializes in what you're looking for: whether it might be a specific role, champion, you name it. Asking about it is a simple yet efficient way, just reach out with a simple "are you able to help me with X". This way you won't have any surprises when your mid lane maining coach hasn't heard about dragons.

Finally, make sure your styles match. In my experience I've had the best experience and seen most improvement with people that matched my approach to the game, my way of talking, my perspective on different things. If you simply can't meet eye to eye on things with your coach, you won't be able to learn much from them.

Look for people without an ego who aren't trying to flex their knowledge or rank on you. Look for coaches who value simplification and communication over "being right". You should be listened to even if your gameplay or concepts are "wrong".

Look for red flags such as hiding rank, saying that they can't help with mechanics, exaggerating things, people who argue a lot with others or try to bring other coaches or players down. Also, in my opinion, you should look for the highest ranks possible such as Challenger, a lot of people call Master/low Grandmaster high elo but in my opinion it's not enough to coach to a really good degree. Unless you want help on a specific champion, don't look for OTPs, and look for people who play as many roles as possible and have not only deep but also wide knowledge.
A good coach is professional and not arguing a lot.

I think it's hard to find a good coach. If you are Iron to Diamond player and you pay 10 bucks to the Master player to go over your gameplay you might learn absolutely nothing.
You might pay a Challenger streamer that is a really good player themselves a 100 bucks and still learn nothing. To go over the gameplay itself, can be done by a lot of players that are bit more higher ranked than majority of the player base.
However, to actually learn about the game and make sure the processes are understood it takes someone that know how to coach and guide someone. As opposed to showing them X and Y - telling them to do this and that. That doesn't help. It really, rarely accomplishes anything. I hope someone is able to look at the interviews here and find someone that fits what they expect!

Something like a good coach is very vague as a good coach for you could be a bad coach for someone else. You need to find one that works for you so when hiring a coach, during the first session or introduction try and see if this is going to be a good fit, not just a good coach but really a good fit, does the coach suit your personality, playstyle, ... ? You can also ask the coach before the session after his approach, personality... . Get to know the person behind the coach :). Look for clues in his responses, ... . A good fit with the person 'behind the coach' is an absolute necessity if you want to get a lot of value out of your sessions.

For hiring a coach, make sure that you find someone who is a good and focused coach, rather than a player. Being high ELO as a player doesn't always correlate to being a strong mentor and being able to break down concepts and ideas in a way that you can learn from them. Your personalities and goals have to line up.

The other most important thing, is that you will get out of coaching as much as you put into it. You need to listen closely, check your ego, open your mind to new ways of thinking about the game and plays, and put in a lot of practice and repetitions with the advice and wisdom given.

The best advice is to find a coach who can help you with your specific role or champion if you are OTP. Also, make sure the coach you want to hire is experienced with at least +200 students. Sometimes coaches are good players but they have no idea how to share knowledge properly and they won't help you. So you need to find a good one by doing some research.

In the end, your effort will correlate to improvement. Even if you hire the best coach in the world but you don't put enough effort into improving as a player, you won't notice any difference. Keep in mind that!

Hire a coach once, understand what you need and if he's understanding your issues. there's no other way if not to test him out once! If you feel pressure or after lots of time nothing is improving change and test again maybe you got unlucky or his style it's not appropriate for your situation! It doesn't mean that the coach is bad, simply, he could be specialised on something else.

Just make sure he's not Too toxic. and make sure he's a friendly guy who knows how to Teach. more than knowing how to Play.
most players that are master+ are gonna easily be good for any low elo player anyway. but not even challengers could be pretty bad at explaining things or coaching someone. so it really comes to the skill of Teaching.