Before going any further, it might be helpful to read the article on "planetary units". We use a series of clutches and bands to "hold" appropriate components of a compound planetary gearset. Through different combinations of holding and releasing planetary components in a compound planetary gearset two gear reductions, a 1:1 ratio, reverse, and an overdrive ratio are possible. These clutches and bands are applied by hydraulic pressure. Obviously, if we apply the components with hydraulic pressure, the first thing we will need is a hydraulic pump.
So the torque converter is nothing more than an alternative to the connecting and disconnecting the engine from the drive wheels with a clutch assembly, such as is used in a stick-shift transmission, and the planetary gearset, is merely another way of producing torque multiplication, and reverse direction rather than using conventional gears (again, like the ones used in a stick-shift transmission).
In the case of a stick-shift transmission, all selecting of gear ratios (shifting) is done by the operator; What gear to be in, when to upshift, when to downshift. The operator does this usually by "feel", "sound of the engine", or by a tachometer or speedometer. When idling through a residential section, (as if looking for an address) the operator will usually choose to upshift very early (low engine speed). When accellerating from an intersection, or up a freeway on-ramp, the operator will usually choose to upshift relatively late (higher engine speed). When passing another automobile, the operater will often choose to downshift to accellerate more swiftly, then upshift again when the automobile is passed and the operator's vehicle is no longer accellerating. All of these decisions require thought and decision-making from the operator of the vehicle. In an automatic transmission, these "decisions" are made by a series of hydraulic valves, channels, and in more and more cases, electric solenoids (on/off valves similar to a hose spicket, or more accurately, like an electric sprinkler valve, turning on or off depending on whether they have electrical power or not).
We first need a way to "tell" the transmission how fast the automobile is going. This is done with a device, called a governor, that rotates in relation with the drive wheels. The governor has weights that "fly out" by centrifugal force; The faster the governor rotates, the more the weights "fly out", and as they do, they move a valve. Fluid pressure is directed at one side of the valve, and as the valve moves, it allows some of that pressure to be directed to another passage; how much pressure, depends on how much the weights "fly out" which, of course, is dependant on the vehicle's speed. This pressure is referred to as "governor pressure"....how original.
Now we need a way to monitor engine load (how much the operator wants to accellerate). This can be done many ways, but the most common ways (in a non-computerized transmission) is by means of a mechanical link to the throttle, or a vacuum-sensing device (called a vacuum modulator) connected to the engine. The mechanical link to the throttle is more commonly referred to as TV (throttle valve) by professionals, and "kick-down" by "shade-trees". TV operation is simple; the farther the throttle is depressed, by the operator, the more a cable or a rod pushes or pulls on a valve. Like the governor valve, fluid pressure is applied to one side of the valve, and when the throttle is depressed, the valve is forced in a direction that allows some of that hydraulic pressure to be directed to another passage. Now for your first quiz: What do you think they call the pressure that is directed to that passage by the TV valve?.........TV pressure. The vacuum modulator works similarly. As the throttle is depressed by the operator, engine manifold vacuum drops. This vacuum acts on a diaphram within the modulator, moving the modulator valve. One side of the modulator valve has hydraulic pressure from the pump, and as the valve moves (under low vacuum conditions) the valve allows more hydraulic pressure to be directed to another passage. This pressure is also referred to as TV pressure, or modulator pressure
Ok, to put things into perspective. The operator puts the transmission in "drive" and begins to accellerate the engine; The vehicle begins to move, and the governor weights begin to "fly out" as a result of the spinning drive wheels. The TV system or vacuum modulator, reacting to the throttle movement of the operator, increases "TV" pressure; A small amount of pressure for light accelleration, and a progressively larger amount of pressure for increased accelleration.
When first starting out, it is logical to have the transmission in "first" gear, and that is just what the job of the transmission valve body is. The valve body is just a "chunk" of metal with a bunch of valves (all with different jobs) all in one piece. The first valve to consider is the 1/2 shift valve. A spring contacts the valve on one end and holds the valve in the "1" position (first gear), and governor pressure is directed to the opposite end of the valve. As governor pressure rises (with increased vehicle speed), it "pushes" on the valve; When this pressure is great enough (vehicle speed has risen sufficiently) it overcomes the spring pressure, and the valves moves to the "2" position. Fluid is then directed to all of the clutches and bands that hold the planetary components required to make 2nd gear. Now, TV pressure is also directed at that valve, opposing governor pressure. The higher the TV pressure, the higher the governor pressure must be before the valve will move towards the "2nd" position. Also, when already in the 2nd position, the operator may increase the throttle setting, and if that throttle setting is increased enough, may force the 1/2 valve back to the "1" position, causing a downshift. Some people refer to this as "kickdown".
The next valve to consider, is the 2/3 valve. Like the 1/2 valve, the 2/3 valve typically uses a spring on one end, and uses governor pressure acting on the other end; When governor pressure is sufficient, the valve moves over to the "3" position, and Voila! Third gear. As before, TV pressure also acts on the valve, opposing the pressure applied by the governor; The higher the TV pressure, the later the upshift, and as with the 1/2 shift valve, If TV pressure is quite high (heavy accelleration), the valve may move, commanding a downshift to 2nd from third.
I should probably point out that I am leaving alot of details out, to make this whole hydraulic system seem less complicated. We can build on this foundation later.
This is basically how a transmission "decides" what gear to be in, but there is much more to it than that.