On any gearbox, one half of the gear set - either that connected to the input or output side - will be fixed to its respective shaft. The other half of the gear set will be free to spin on its shaft until one of the gears at a time is locked onto the shaft, to connect the input and output shafts together.
The system used on road cars is called synchromesh and allows smooth and quiet gear changes. Each of the gears has an angled cone attached to it, as well as a series of drive teeth on the face. There is also a ring, with a series of drive teeth, fixed to the shaft and when a gear is selected, a grooved collar slides across and joins the two rings of teeth, or dogs, to lock the gear onto the shaft. Force is applied to a cone on the gear by the sliding collar and this equalises the speeds so the collar joins the two rings smoothly.
The gear change is relatively quick. But in motorsport, where every second counts, it's not quick enough. So to speed up gear changes, a different system is used, called dog engagement, hence the term 'dog gearbox'.
Here, the speed-matching synchro system is done away with, and the relevant gears are locked onto their shafts using a dog ring. Again there are a series of dog teeth on the main gear and a sliding dog ring on the shaft, with splines to drive it. However, there will be anything from three to six dog teeth on the ring and the hub. The large teeth and gaps mean that the ring and hub will engage almost instantly and the gear change will be as fast as the lever can be moved.
The teeth have a slight undercut angle on them, so that while the engine is under load, force holds the dogs together. However, to change gear, this load must be removed, so either the driver must lift slightly or there needs to be an engine ignition cut-out switch. This will briefly cut the ignition, remove the load and allow the engaged dogs to separate. Normally, a dog box may not need the clutch to change gear, but it does need the right technique. The driver needs to be positive with the lever or the dogs will just bounce off each other and the gear won't be selected.
There are two main methods for actually changing gear: an H-pattern shift, as on most road cars and a sequential shift, as on most competition cars.
For H-pattern gearboxes, the lever is directly linked to the selection forks, whereas a sequential box has the lever acting on a rotating drum with slots in the surface, which move the selector forks. The advantage of a sequential shift is that it eliminates the possibility of missing or mis-selecting a gear, as you can only change one at a time.