Sorry if I confused you, this is part of my day job so I deal with it all the time, albeit from a design side.
The Automatic Transmission Fluid (ATF) filter is typically located in the transmission oil pan. Oil is taken from the sump and pulled into a pump, usually driven by the torque converter. It is sometimes changed when the fluid is changed. In modern transmissions, they are always changed together.
The valve body controls when and how the transmission shifts. It looks like one of those 3D puzzles where you move the ball through tiny passages. Fluid pressure changes as the RPMs increase (because the oil pump is driven by engine speed, remember) which moves check balls through various passages which alter the fluid flow through the valve body. In an older transmission such as this, the system is controlled exclusively by fluid flows. In more modern units, there are electric solenoids which also control the flows, and therefore the shifts.
The valve body is also usually accessible via the transmission oil pan. It is comprised of a series of sections joined by gaskets. If any of the ports between sections become fouled, it will affect the shifting.
