I went from private farm land to public hardwoods 8 years ago. Wow, it's very different. I had to relearn how to scout and what to look for in deer sign.
Here's how I got started and what I would recommend. I checked out a couple of public land areas closest to me and picked one. Then I spent time learning it. I haven't set foot on all of it, it's big, but I've had boots on the ground over a lot of it. Another hunter I encountered during my first few years gave me this advice, pick an area and focus on it. That was excellent advice. I'd simply add to it, spend some familiarizing yourself with the whole area, use google maps, topo maps, and just get out in it. If you're like me, I want to be away from other hunters. I not only looked for spots other hunters would avoid, mostly due to distance of the walk, but I also observed the patterns of other hunters. Once I found an area that I liked, deer sign, fewer hunters, etc, I focused on it. It was 5 years before I killed a deer there. I didn't kill in year 6, killed again last year and I've tagged out this year. It's rewarding to know you've been successful on public land where it's tough hunting.
I'd like to add one more comment about other hunters on public land. That was my number one concern about hunting public land. However, all those that I have encountered have been friendly and courteous. Those with experience have been willing to share advice, without giving up their spots. On top of that, the biggest buck I've killed, a 140'sh deer, came out on the same path as another hunter, who had exited the woods about 45 minutes before the deer. We were both about a mile from where we'd park and I had no idea where he was or that he had gone in further than me. I never met or spoke to him. He politely smiled and waved as he walked out past me as quietly as he could. Since I'd planned to sit all day, I decided to sit it out. It was well worth it.
Good luck!