A dog gear is a mechanism for shifting. It rides on a shaft, preferably hex but I'm sure keyed works, too. The dog has three teeth on both faces that fit into pockets on the side of special gears. The trick is that there are two gears on the dog's shaft, one on either side of the dog, and the dog will engage one of them. The other one doesn't spin at all. You can slide the dog back and forth along the shaft to determine which gear it's driving.
Take a look at the AndyMark Super Shifter:
http://www.andymark.biz/am-0114.html