Start with something easy

Most of people don't like changes, or maybe in different way - they like, but only if changes won't have any impact on their current life and doesn't require additional effort. Unfortunatelly those kind of changes happens rarely, if at all.
It doesn't matter do we talked about improvements, development or solving a problems - if we want to do something, it will always require to move people from their safe zone. Even if we plan to fix an issue, most of people will tell you something like: "yeah, we should fix it, but maybe not now, maybe it's not so important and, to be honest, I get used to it and I can live with this." or: "we shouldn't do anything, because after ... problem will solve itself."

Well, problem won't solve itself, we need to do something to make it happen and if problem affect us somehow, solution also will. We cannot avoid it.
"Living with it" isn't a solution either. Sooner or later you need to handle the problem and if you won't, it will be someone from your team. This is not a solution, this is postponing. The later you start to handle the issue, the more difficult it will be to solve it.

So what to do if you are in situation that is worth to introduce changes/improvements/fixes and you need to convince people to follow you?

If your team already working in culture of continuous improvements then it's easy, you just need to show them reasonable arguments and they will at least try, they will put they effort to check whether the idea is good for them or not.

But what if you are far from it? What if they worked for many years without changes and they just used to this "complain and no action" state? Maybe they already talked about the problem many times and even agreed for solution, but it required lot of work and they just weren't motivated enough to finish it.
Situation like this have more negative impact, because problem still exists and additionaly team is demotivated, they felt they already made steps to solve the problem. It's not important they didn't have strength to endure to the end.

start with something small to succeed fast

When I'm start to work with new team or group of people I always do recognition, try to find the problems, bottlenecks and places for improvements. I also look at all people who would be affected because of potential change or who are affected right now because of existing problem.

When I have all those information, I'm trying to think about solutions for problems (only ideas, without details, just not-binding propositions). But not all of them at once, I'm starting with the easiest one. And the easiest doesn't mean unimportant.

After preparations I'm scheduling a meeting to talk with the team. At first time, we aren't focus on solving any issue, we just talk about them. I heard many times that is no more than waste of time, because on first meeting I don't have plan to get any conclusion, but in my opinion, this allows them to share their's problems with me, we are starting to build relationships and trust.
And this is the reason for this meeting - if I want to help them, they need to know I do care.

On next meeting I present them the list of issues and proposition for improvements. We are prioritizing them and after it's done I'm looking for the most important from the easiest. The one, which requires the lowest amount of effort and time to implement. Why?
If team have wrong experience with doing a changes, you need to prove them that is important and it will pay off. You cannot be another person who will promise everything and will leave them with nothing.
Even if they are eager to do changes, because you are the person who really know how to talk with people and know how to convince them, you still should start with something easy. The less experienced in well done changes team is, the bigger risk for failure. We want to minimize this risk, we need to give them experience, the fastest and shortest way is to start with easy problems.

The more things you will solve/improve, the most experienced team will become, the more effort and time they would dedicate to implement it. If they will see the results, they would be more open for further changes.
Each success will prove them that it's worth to invest their strenghts to achieve the goal, they will decide for longer term changes without fear and with motivation.
They will trust you, so it won't require as much effort from you as on the begining to convince them for next step.

Start with something small and you will achieve great things.