I personally like to use forks when I'm breading, so that I don't have to keep reaching into the containers. I use a pair of forks in each containers, which I use to move the food around 'til it's coated, and then lift them to drop into the next container (important -- the forks should not go into the next container ... grab from one end, lower in, but release before the forks touch the stuff in the next one).
You can also use chopsticks or tongs, but I prefer the forks as I can use them to scoop up a bit of flour or breadcrumbs to sprinkle on the bare spots of whatever I'm breading.
- Prep all of whatever you're going to be breading first (assuming you're cooking alone, and don't have a helper). Having to wash up because your hand's all chicken-y really slows you down.1
- Never go backwards. Yes, some people like to go back into the flour, but if you're looking to be mess-free, don't do it.
- Shake off items before going into the next container ... you want a minimal coating of everything -- flour won't stick to flour, so shake off the loose flour before going into the egg. Let the egg wash drip for second or two before going into the crumbs, and shake off the loose crumbs before going into the pan. This will both create a crust that won't separate from the food as easily, but also prevents that growing cluster of crumbs forming in the third container.2
If you're looking to do some breading with the kids, and the kids are too messy, the crumb and flour can be placed into paper bags, and you drop items in, seal up the bag (fold over + binder clips), and then let the kids shake the bag. You might also be able to use containers with a tight-fitting lid. It'll slow you down overall, but it's no worse than the constant 'I want to help' pestering.3
1 You'd note that I said "hand" and not "hands." I keep a strict rule that whenever possible, I only touch raw chicken with my left hand, so that my knife hand never gets slippery (and so I can grab the phone if need be without washing up).
2 Some people also disagree with this step, as in the case of fried chicken, you don't get those extra crunchy bits on the outside. There is, however, a solution ... take the fork in the egg wash, and let it drip into the crumbs, then use the crumb fork to coat them, and lift them to the top of the container ... then set the item to be breaded on top of them as it comes out of the egg wash.
3 Before you worry about me suggesting that I have kids and I consider them pests, no, I don't, but I frequently cook at a friend's house and they do, so we have to set up the breading station away from the stove so that they can help (at home, the crumbs would be right next to the hot pan). Although some people put the crusted objects on a tray or wire rack and let the eggwash dry for a few minutes to reduce crust separation.