Here's a list of some of the foods to experiment with:
Any good quality aquatic turtle food is a good staple
for your snapper. I've found that larger, floating pellets work best since
they are easy for your turtle to find and for you to clean out in case,
for some strange reason, it's not hungry that day. Stay away from the stuff
that looks like fish food. It usually sinks right to the bottom. Also avoid
the paste type foods. Since aquatic turtles eat only in the water (that's
the only place they can swallow their food), the paste foods that have to
be scooped out onto a rock don't work too well. Not only does your turtle
have to find the food, it has to pull it into the water where it quickly
dissolves and makes a huge mess. Trust me on this one.
Some common brands are:
Any lean, COOKED, meat will be fine. It has to be cooked.
If you give your turtle raw chicken you can bet that everyone that comes
into contact with it will get sick. And if you decide to just give it a
piece of what you are eating, make sure it doesn't have any spices, oils, ketchup, or whatever.
Turtles get belly aches too!
You'll have to play around here to see what your snapper
likes. Bahamut enjoys bananas, oranges, tomatoes, carrots, water plants
(from the river near where he was caught), and even broccali (better him than me).
Just put a little of whatever you might be eating for dinner (before cooking and
dressing) in it's feeding tank and see if it eats it.
Feeder goldfish or minnows *(see important note on goldfish at bottom!), red worms, night crawlers, shrimp, meal worms, crayfish, minnows, salamanders. Basically any small fish, insect, or amphibian that might live close to a river or pond. Now some of these depend on the size of your pet. It would be just plain evil to put a feeder goldfish in the tank with a baby snapping turtle. YUCK!
When it comes to live foods, I give Bahamut minnows and crayfish an occasional treat. At a petstore the minnow only cost something like 9 cents each and he really enjoys them. I prefer using minnows over goldfish because I can catch them myself and when I do get them from a petstore they are gennerally in better shape that the feeder goldfish. Also cuts down on the "awww" factor from my wife.
It's very important to get your live foods from a good source. The feeder minnows you get from Totally Fishy can be completely different from those you get at Uncle Earl's Tackle and Tobacco. Here's a mini-guide to getting live food:
I've got a nice little memory (taking up space that could be used to help me pass my computer vision class) of a pet 'joint' in a town I used to live in. Perfect Pets I believe was the name of the place. You walk in and you're taken aback by the smell of unclean ferret cages and mildew. Just glancing at the cloudy fish tanks, unclean and unheated reptile tanks, and 4 guys standing at the checkout counter (it looked like Larry, Darrel, and Darrel found their good buddy Steve) convinced me not to buy anything from this place.
If you're buying feeder fish or other aquatic live food, you'll most likely have the best luck from a place that specializes in fish. Find out where the aquarium gurus go to buy their $400 fishies. Look for clean tanks with clear water and healthy fish. The place I get my feeder minnows from takes the same care of their feeder stock as their other fish. It's important that your feeder fish be as healthy as possible to help avoid making your turtle sick. If there are a good deal of dead fish in the tanks, find some place else.
If crickets or earthworms are on your shopping list, a shop that handles a good number of reptiles would probably be your best bet. You will probably be confronted with a few choices when it comes to crickets: small or large, dusted or not. I'll bet you already know the difference between small and large don't ya? OK, fine... straight to dusted or not. You want 'not dusted'. Easy enough. Basically, (you knew I just couldn't not explain) dusted crickets are coated in a powder that supplies extra nutrients. Dropping a dusted cricket into a tank of water not only makes a mess, but also defeats the purpose. Other than that, it's hard to go wrong when buying crickets.
You'll want to ask a few (well one) important question about earthworms and that is "What were these worms raised in?" If they don't know, ask them to find out. You don't want earthworms raised in manure. If you can't find out, you're probably better off getting the worms yourself.
Keep in mind that insects aren't the most nutritional of foods. Gut loading (feeding the insects good veggies with some vitamin powder) helps but still try to use insects as a treat and to add some variety. A mainly insect diet is not a good choice.
Bait shops:
If you can't find a decent pet shop and you don't like the outdoors, then you can try a bait shop. It's probably not the best choice but you might get lucky. Bait shops usually have a wide variety of live foods. Minnows, night crawlers and red worms (large and small earthworms), wax worms, meal worms, crickets, leeches, salamanders, etc. The catch is, they are not usually kept in the best condition. Most bait shops add a good deal of chemicals to the water they keep their minnows in. It's usually a bright blue. Also, the earthworms are usually raised in manure. The main difference is that the live food you get from these shops are not meant to be food, they are to be used as bait. It's not a big deal with wax worms, meal worms, or crickets, but this would probably be a bad choice for minnows or earthworms. You can always ask about the living conditions but expect a chuckle.
The Wide Open Spaces:
This can be a fun option in the spring and summer months. Find a good, clean location. Avoid the little gray stream outside your apartment complex. Urban areas are not a good place to find healthy live food. You'll probably have to go out of town. Everyone probably knows or can figure out how to turn over a rock and pick up a worm so I'll skip that. The aquatic prey may be a little harder though, so I'll provide the super complex plans on how to make a minnow/crayfish trap. Warning: Do not attempt without at least a BS in Engineering.
Plans for Eric's Trusty Ol' Minner Trap:

What's too skinny? Well remember this is an aquatic turtle that DOES NOT go all the way inside it's shell. If it's skin starts to look loose and baggy, feed it! Don't worry, you will be able to tell.
How much should you feed it? You can't go by the info on the turtle pelet containers, many say to feed it every day, until it has eaten all it can eat in 10 minutes. If you do this even only once every three days, your turtle will explode! The best method I have found is to feed your turtle until it begins to slow down its eating. If it stares at the food a while before snapping it up, it's full and only eating because well.... it's there. Expect your turtle to start snapping up the food very quickly at first, and then begin to slow down considerably as it fills up. You will just have to experiment here. Again the skinny rule applies.
How do you feed it? Well, if you're using floating pellets, just toss 'em in a few at a time until your turtle has had enough. Most live food is handled the same way, with the exception of earthworms. They sink fast If you want to hand feed your turtle use tongs or hemostats instead since your hungry snapper will most likely have no regard for your delicate little fingers.
* Tip: Now take note here, this may be the best feeding advice I can give. Use a separate feeding container. Get an appropriately sized Rubbermaid storage tub (I use an 11" (Height) X 13" (Width) X 20" tub) add some water (enough to at cover your turtle plus some), turtle, and food. Clean up is a snap (just dump the water out so don't use too much. It's wasteful and heavy), food is easy to find, and your turtle's enclosure stays MUCH MUCH cleaner. If you ignore every thing I've said listen to this one.
* Warning: If you feed your turtle goldfish, take note that they may carry bacteria that can harm or kill your turtle. To help prevent this, try freezing the goldfish (of course you will want to thaw them before serving ;) ) or use feeder minnows. This important information was contributed by Doug in Boston via e-mail. Sorry to hear about your alligator snapper Doug.