At the MG Owners Club HQ at Swavesey is a cutaway gearbox and rear axle. So when we were there at the weekend I thought the photos would be handy.
So first the gearbox internals. This is a standard four speeder, but the principle is the same for all conventional boxes. This is shaft in/ laygear/ shaft out. For reverse gear there is an extra shaft & gear between the laygear and output shaft, which reverse rotation of the output shaft.

The clutch is visible to the right. Out of the centre comes the first motion shaft/input shaft.The first helical gear inside the casing is an integral part of the shaft and manufactured as one piece. In the end of this shaft is a hole, a spigot hole, into which fits the forward end of the third motion shaft/output shaft, either using a plain bronze bush, or needle roller bearing.
So on the top row, starting at the left, is straight cut reverse gear, first gear, first/second gear synchro hubs and baulk rings, second gear, third gear, third/fourth gear synchro hubs. You can see that the engagement dogs for each gear match the dogs on the synchro hubs. This gearbox is in neutral. When first gear is selected, the left hand synchro hub moves towards the gear until the dogs are fully covered. Each gearwheel rotates freely on the third motion shaft, but the synchro hubs are locked onto the shaft and rotate with it at all times. The selector forks are the two inverted U shaped pieces visible at the top, and are semicircular. They straddle the synchro hubs and are usually a hard wearing bronze type material. If you ride with your hand on the gearstick, this is the part that will wear.
Underneath is the laygear, which is a single piece of material with all the gears machined from the solid piece.
So the drive comes in from the right and is taken up by the right hand gear on the laygear. The laygear turns each gearwheel on the output shaft/third motion shaft/mainshaft. Remember that they are free to turn until selected by the sychro hub. The selector mechanism has an interlock which prevents engaging two gears at the same time, but when this wears, that can happen, and the gearbox will lock.
First gear on the laygear is the far left, so you can see that the small laygear acting on the large first gear gives the low gearing for first. For fourth gear, the right hand synchro hub moves to the right and locks the input shaft and output shaft together, so both shafts act as one, and the laygear simply idles at the bottom, turning all the gears, but none are transmitting drive. So fourth gear has no gearwheel.
Out of sight behind the laygear is reverse gear. This is shaped like the capital letter i. Two straight cut gears separated by a shaft, but a single unit. When you select reverse, and most are straight cut and without synchro (which is why reverse crunches), reverse gear meshes the straight cut gear on the third motion shaft with the straight cut gear on the laygear. The extra shaft reverses direction of the third motion shaft, and you have reverse.
The rear main bearing is far left, and is massive. The front bearing is not visible but is smaller. The whole thing is adjusted with thrust washers to minimise endfloat, and that's why it's good to change the oil occasionally to get rid of metal filings.
Now the axle. This is a Salisbury, and simpler to describe than the gearbox!

The pinion runs from the centre of the photo to the right and sits in two bearings. The gear is the size of a large bun.
The crownwheel is the large gear, and is fixed to the blue cage. Inside the blue cage are the pinion gears and the halfshaft gears, in permanent mesh. You can see the pinion pin, the alignment is ENE to WSW, and the pin is retained by a small rollpin, the hole is visible. It's hard to visualise how diffs work, even with a photo, but with traction to both wheels, the pinion turns the crownwheel, and the cage rotates with it, so both halfshafts rotate at the same speed. If one halfshaft speeds or slows, the four small gears rotate about themselves in the cage. If you take the cover off your diff you can watch this in action, but even then it's hard to grasp what's going on. Limited slip diffs are more complicated than this!
Any questions?