How do I become a good bowhunter, especially on public land?

The best way to get better at anything in life is always the same - practice, practice, and more practice.  Unfortunately, there is no "practice" in bowhunting, which means you just need to get out in the field and start doing it.  You will learn more from spending time in the field and having real-life experiences than you will through any tv show, podcast, or YouTube video.  Pay attention to your surroundings while you're in the field - focus on where and when you see deer sign, how deer behave, where and when they are moving, what they react to, etc.  Nobody becomes an expert at something overnight so give it some time and pay attention while you're out there.