Adult snapping turtles can be hard to spot unless you're right in there with them. Sometimes you will see a flash of carapace in the shallows where they are hunting for food. If this is at a lake edge, you usually have no other choice but to charge in there after them. Normally, they will shoot for deeper water, and if you're quick you can grab the back end of the carapace. This goes without saying ...DON'T grab them or pick them up by the tail.
Once grabbed, they will forcefully kick back and catch you with their sharp claws. Sort of place your hand on the plastron while gripping the edge of the carapace and lift them out of the water. If they are a manageable size, hold them kind of cradling in your forearm with the plastron facing up and away from your body. Bring them to land. This takes a little practice. Sometimes the turtles is too large to do this, and we used to use potato sacks to wrangle them. We would walk through a river, carrying giant common snappers in a sack until we reached shore. Common snappers can be found in most bodies of fresh water including rivers, ponds, swmaps, and lakes. Look for them basically any time during the day. Good luck.