The Basics: Planetary Gearsets

Planetary gearsets have been used in automatic transmissions and overdrive units since the beginning. They are inherently stronger, for their weight, than a comparable "two gear" setup commonly seen in a stick-shift transmission. Planetary gearsets are made up of three components, all in constant mesh; A sungear, A planetary carrier and planets, and a ringgear or internal gear. When one component is held stationary, and another component is rotated, the third is driven at either a reduction , or an increase in speed, or a rotation in the opposite direction. (did I say that right?).
The planetary gearsets that are commonly used in today's automatic transmissions are actually "compound planetary gearsets" because they are basically two planetary sets that have common parts. Most 3 speed transmissions, for example, use two ringgears, two planetary carriers, and a common sungear (all one piece, but long enough to mesh with both planetary carriers.) By changing which components are rotated by the engine, and which components are "held", two different gear reductions (1st gear, and 2nd gear) and reverse, as well as a 1:1 ratio (third gear) can be obtained. These "holding" devices, are more commonly known as clutches, and bands, and one-way clutches (roller clutches, or sprags). One-way clutches, are clutches that hold in only one direction, and freewheel in the other, like the freewheel on a ten-speed (I guess in this day-in-age its 12 speeds and 18/21 speed mountain bikes, but you get the idea), or a ratchet wrench. These one-way holding devices allow the planetary component to be held under acceleration, but to freewheel under deceleration.

You learn to appreciate a one-way clutch when you are approaching a stop sign, and as the transmission downshifts, you are not thrown forward, like you are when someone suddenly downshifts in a stick-shift equipped vehicle. The one-way clutch just freewheels, until the car comes to a stop, then locks to hold the component, creating a gear reduction to get the car moving again.
Let's use a typical 3 speed automatic transmission(A C4, Torque-flight, etc.) to help illustrate what happens as the trans goes through the gears. First, as the trans is shifted into drive, the forward clutch (cleverly named, because it is used in all forward gears) comes on, and the low one-way clutch holds; You have 1st gear. When it is time for second gear, the front, or intermediate band is applied; the forward clutch is still on (the car is still moving forward), and the one-way clutch freewheels, and Voila, you have second gear. When third gear is needed, the direct clutch comes on and the band is released, the forward clutch is still on, and the one-way clutch is still overrunning; You have third gear. When the shifter is in the reverse position, the forward clutch is off, but the direct clutch is on and the reverse band is applied. These clutches and bands are used to "hold" the different components of the compound planetary gearset, and different combinations of "held" components will yield different combinations of gears.