Hunting public land can be a challenge for any bowhunter. Number one, you need to find areas that are not being pressured heavily. If you can't, you will not be able to hunt natural movement patterns.
Look for the most remote and inaccessible areas. Most people are not willing to work hard enough to get to such areas. Examples are spots that require a boat to access or require a long walk or a climb up a steep bluff. I know there are some public areas in many states that fall into these categories. Once you find such areas, you should be able to use typical hunting strategies that you read about on this website.
If you can't find low pressure spots, you have no choice but to pattern the other hunters and rely on forced movement from the deer. Figure out where the other hunters enter the cover, how deep they hunt and then get in ahead of them.
Enter by a different route so you don't alert the deer. Plan to hunt escape routes, funnels between where the hunters are coming from and the nearest sanctuary, possibly nearby private land. Simply put, you just set up where the deer are most likely to exit and let the other hunters drive them to you.