Well, I don't have any specific strategies or methods. I could say 'make more games', but as you noted that isn't very specific. The thing is though, like anything else it is practice which allows you to improve. Although practice isn't all of it, you also need feedback so you can adjust.
One of the first minigames I did professionally involved a lot of back & forth with an artist, a designer, and just getting feedback from other co-workers. I paid attention to what worked, what didn't and, most importantly, what worked better/worse after I changed it. A few years later I did a game that was basically a collection of mini-games that let me practice what I knew in a small area. Although I am a long way from the skill of some of the designers I know, it has allowed me to understand and design better than I could before (I can identify reasons why something might work, and I can pull from solutions to design problems because now I have a basis).
As a programmer I have improved from writing code for a wide variety of problems, and from working with others who were very good programmers and had interests divergent from my own. To give a specific example of that, my understanding of c++ templates. I worked with another programmer who was very good at what he did, and we be described as one of the folks with the standard. From that I had plenty of opportunities to not only ask him questions, but to pull apart complicated template code and understand how it works. I went from a minimal understanding of c++ templates (I could create a data structure) to a strong grasp (I have a strong understanding of SFINAE and do some pretty neato tricks).
To a much, much lesser extent another influencer is playing a variety of games with a dev eye. I had a game that stalled, however some time later I played a game that, although very different from mine, the way the avatar moved actually solved the biggest problem I had had. If I were to ever revive the project, I now know how I can solve that issue.
So ya, I don't have any specific strategies. Just practice and get feedback.