The best way to learn to build products is to—build products. There is no substitute for it. Nothing else quite exercises the same muscles. With this in mind, how can you improve at product if you aren't doing it at work?
1/ Hack on side projects. Side project are unrelated projects you do outside of work. They don't need to scale or last for months—a weekend is fine. You can build and break them down quickly once you've accomplished what you set out to.
I like picking a small, achievable version of a problem to solve, solving it, then deciding whether or not to improve it further.
The reason why side projects are so powerful is that you own the whole process from ideation to implementation. You decide when something is good enough, and often have to solve open-ended problems that are relevant to you.
Lastly, side projects need at least one user to be effective. That user could be yourself. Products that are built in a vacuum usually don't succeed when released to the real world. The process of gathering feedback, iterating, and releasing something new is hard to emulate when you aren't working with real users.
2/ Write about products. Pick a product you use and write down why you use it: What makes it delightful? What could be improved? Why do you think it was made the way it was? Think of new features to add.
The process of analyzing others' products is as close as you can get to making them yourself.
Spend some time looking at the website and playing around with the product itself, then write down your thoughts. Now you can check out the discussion and "compare notes" with other commenters.
3/ Talk about products. If you're friends are interested in products, you can chat with them about what they are currently using and why. If not, there are product meetups, where you can do this as well.
Talking about products differs from writing because the medium is very different. When you're writing you have more time to formulate your thoughts. Talking forces you to think quickly on your feet in addition to communicating very clearly.
Product decisions are often made during conversations in meetings, walks, lunch, etc. so you need to be able to demonstrate your product chops verbally. Written communication tends to be a little more thoughtful, but spoken conversation is what dominates the decision-making process.
4/ Listen to others talk about product. It's worth mentioning, but definitely not as effective as the first three points: Listening to product podcasts or other audio, where people jam on products, helps you develop product lexicon. You gain an understanding of jargon and others' frameworks for thinking about products.
This is almost too close to edutainment though. It's very passive and easy to consume, but doesn't require much deeper thinking.
If you want to go this route, I recommend listening to another resource from Product Hunt: Product Hunt Radio. In my opinion, the only episodes worth listening to are the episodes where Ryan Hoover hosts (episodes one to thirty-nine). Here's episode one.
So there you have it! The top four ways to learn product if you aren't doing it as part of your day job.
You might have noticed that I didn't include reading articles or books in the list. While written product content is occasionally helpful, building real products and the real experiences that come out of that process are infinitely more so.
It's like reading about riding a bike and riding a bike.
In order to improve at building products, you simply have to build more of them. The more you build, the better you will get.