I have had pretty good success with eggs and hatching and hatchlings over about 10 years.
I try to notice when and where eggs are laid. I have placed a plastic basket (with open sides, or my kids old toy grocery shopping basket upside down) over the site of the nest for a couple of weeks to discourage predators (I have had coons dig up eggs, and find pieces in the water; I've read that the scent is very strong at first after laying). Then I just try to remember or write down if I've had several layings where the nest is.
Later in the summer, I stroll out to see if hatching is happening. some years I have removed the rest of the eggs if some turtles have hatched and had them hatch inside. Sometimes, if you know where a nest is, after 1 or 2 have hatched but haven't come above ground, the ground will be a little depressed, because the babies take up less space than eggs. I can give more details. If you have a nest that you see turtles have come out of, you can usually tell which eggs are viable. Eggs have to be handled carefully. It's probably best to leave them in ground, maybe putting basket over them (something that won't have a too-warming greenhouse effect or cut out all light).
Some will die, even before hatching. That's sad, if they're nearly ready. Many never develop. I've had a few just fail to thrive after hatching, but not many after my first year or so. Once you get them hatched, though, dealing with the hatchlings poses some challenges. I do bring them inside, in a plastic shoebox with dirt (or sometimes newspapers, though they are a bit dry). Try to give heat (don't burn 'em) I use heading pad with lots of towels, and light. Then try to introduce them to small tender earthworms.....
My general advice is to leave in ground and let nature take its course. But I'm usually too curious and excited if it's close to hatching time.