How does one improve their product thinking skills?

Read and/or listen to books that give you tips on building products. Most importantly use the skills you learn about.

Don't try and do everything in the book. Try and take one or two things that resonate with you and just implement those. Obviously you need to be involved in the development of a product to do that.

For example, I listened to The Mom Test earlier this year. Instead of trying to remember and do everything from the book, I just took one part that resonated. For me that was "Don't talk about your product when interviewing customers, talk about the customer and their problem.". When you feel you've improved at that, move on to the next thing you can improve.

Work somewhere where you have a hand in the process.

Observe and reflect on what makes something good when you go about your life and use different products.

Learn some basic principles of design so you start to develop an eye for some of those concepts and so that you have the vocabulary to express why something is good.

Talk to people about products they use and the processes they have around those products. Honestly, human interaction is the only way to fundamentally improve product development processes.