You have asked a really BIG question and unfortunately, I can not answer it in "25 words or less", and I may not be able to anwser it satisfactorily for your purpose. Your best bet is to go to a college or library that has mechnaical engineering textbooks, and look up automtive transmissions. Look for cut-away drawings showing the action. A few repair manuals, especaially the ones for transmission re-building, may have the information you require.

But, I suspect you did not wish to delve this deeply into the innards of a transmission. I will try to give a short version.

A manual transmission is intricate, but has easy to understand, straight forward gearing; Automatics are more intricate and use planetary gear arrangements consisting of a central or "Sun" gear, a carrier holding "planet" gears against the sun gear, and third outer ring with internal teeth with which the planet gears ride in. Now, consider these three elements or subassemblies: Sun, planets, and outer ring; To transmit motion, one element is "fixed", one set driven, and the third is the output. So, for a single set of planetary gears, 3 different speed ratios are available depending on which element is locked, and which element is driven. One of these combinations will have an output rotation that is the reverse of the input. By stacking two sets of planetary gear systems on a shaft and hooking one to the other, a variety of gear ratios are available including reverse.

Now, what you wnated to know, is "How does all this claptrap work?" The elements are held or allowed freedom by a system of cluthces and bands. These clutches and bands are hydraulically operated. Smaller 'servo valves' control the larger hydraulic actuators and select which ones to lock. To change gears, one set must unlock while a second set locks. Smoothness of gear change depends on critical timing between these two actions.

The automatic transmission has had a long history of development and improvement. In the 1930, an electric solenoid shifted transmission was available for the Kissel brand made in Wisconsin. It was shifted by pushbutton. That one was a "slam dunk clunker" and was not a marketing success. It and the Kissel car died during the depression years.

The next, and more successful automatic was developed by the Oldsmoblie division of GM. GM named this transmission the "Hydraumatic" and it had both a fluid coupling and a torque convertor. Drivers got the impression it had 4 speeds, but what it had was 2 geared speeds and 2 more apparent speeds depending on locking or unlocking one of the fluid drive elements. This combination gave 4 apparent speeds. That transmission was a nightmare to keep in adjustment. In the 1950s, The Chrysler Corp. deveolped an automatic and dubbed it "Torque-flight". As the years passed, improvements on that transmission made it a sucessful offering. And of course, Ford had their version, too.

The next major development was the addition of lockup clutch on the torque convertor. This cut the fluid drive losses and improved fuel mileage.

All went well until about 1989 when better microprocessors became available for automtive applications. Chrysler redesigned their transmission and put the lockup clutch inside the transmission case. The hydraulic logic for shifting was replaced by electronic control and trouble popped up. A new round of development began and it took about 10 years to find a winning combination. Ford and GM managed to avoid much of the bad shift problem, but had their share of other electronic and sensor problems.

To sum it up, it is not "smoke and mirrors", but rather shifting is accomplised by the coordinated action of locking and unlocking a set of clutches and bands to select the input-output ratio. These friction elements are the major wear items in an automatic.

OK that's the 'box more or less taken care of, and I take my hat off to jemdandy for such a comprehensive explanation without resorting to jargon. Now how about the torque converter? How does it tell the difference between when I'm sat in D at the traffic lights with my foot on the brake and when I'm, say, trying to pull a real heavy trailer loaded up with bullocks up a real steep hill? I remember in a manual generating some serious clutch smoke on the way back from the cattle mart pulling away up these Co. Cavan hills.

Planetary gears.

http://www.howstuffworks.com/gear7.htm

Here is a link that might be useful: Planetary gear illustration

What a fantastic website Gary. Thanks for that. I want to know how everything in my life works so I'll be on howstuffworks.com quite a bit from now on. Next thing I'll look up will be how the wife works.