Here are the things I’ve done over the years.
Get an actual driving education! There are many skills and driving situations which are not taught in basic driver’s education classes and not required to get a license. They are still skills people should know. Many people are not aware that “advanced” driving instruction is available, but it is, and we’re not talking about racing schools, these are practical driving classes, available in almost every major city. Here’s an example of that: Access2Drive driving school in Queens.
Become a professional driver! There are many professional driving jobs available that don’t require a commercial license, but you can go that route as well, which will require some of that education I mentioned before.
Take every driving experience seriously and learn from it when you can. If someone cuts you off, instead of getting mad and possibly missing something, take a minute to see if maybe you could have let them in, maybe they had their signal on, and you were being a dick about it. Drive defensively, and learn to anticipate what other drivers will do. Study driver behavior in your area and learn how to avoid problems before they happen.
Now I don’t know if I consider myself an expert driver after all that, but with 30 years on the road and all that additional experience, I think I’m pretty good. I think if you do all those things and you make expert driving skills a personal goal, you should be able to be an expert driver in ten years. That’s how long it takes to be an expert in anything really.