my recommendation if youd like to hatch a clutch of wild snappers would be to sit on the bank and scout nest sites, then harvest the clutch of eggs after they have been in the nest for a couple weeks. careful, dont turn the eggs. use as much of the surrounding substrate as you can, and incubate the eggs at the same temperature as the nest (this can be determined with a thermometer inserted into the exterior edge of the nest, at the same depth as the eggs before excavating.) i have done this successfully with several turtle species, red-eared, box, and snapper.
i wouldnt recommend trying to catch a gestating female in hopes of nesting her, as she will most likely re-absorb the eggs rather than lay them in an unfamiliar site.
general rules for catching snappers is very site-specific, but some general rules apply:
know the habits of local turtles, scout their locations/habits.
wade shallows (1-3 ft) barefoot, feeling for 'serrated'rocks.
if you live far enough south that there are alligator snappers, know that there they are grasped differently than commons, and learn the difference in the texture of the caripace.
know by feeling which end is the front!
a snapping turtle, common or alligator, is very docile while submerged, and will not snap (USUALLY) until you surface it.
grasp a common at the back edge of the caripace, just in front of the hind legs, and wade out backward, keeping the hind end elevated above the forend. once on land, BE CAREFUL
with an alligator snapper, determine front from back, and grasp strong hand at rear or caripace above tail, weak hand at front of caripace above head, and lift straight out of water. keep at least the turtles head out of the water as you wade out. if you do not lift an alligator snapper straight up, you will lose it.
it can grab scrub and fight away, and a big'un can swim hard enough to get away from you if you dont get it to the surface fast enough.
BE CAREFUL!!!
but remember, a common grasped at the hind legs cannot bite you, and an alligator grasped at the caripace directly overhead cannot bite you.
this will take a steady nerve, as both will snap AT you, once surfaced, but cannot actually get you, if grasped as described.
HAVE FUN AND BE CAREFUL! LIFE IS BETTER WITH ALL YOUR FINGERS!!