ok - what I figure is you want to know how it pulls a car. A regular shifting automatic transmission uses clutch packs, and planetary gear sets coupled with brake bands to engage different ratios -upshift maybe controlled by a speed governor or electronically by the TCU (speed sensor input) - the torque input is provided by the fluid torque convertor - which also makes the car slip at idle - transmission not moving - when you rev the engine with a gear selected the force of fluid thrusting on the convertor impeller make the transmission turn.
The planetary gear set is a set of gears having three parts.
outer ring gear
planet gears
sun gear
the beauty of this piece is that you can hold one part still , move another and take output from the last piece.
As for CVTs there are two variants, one is a belt type technology (to figure it out go visit a lathe shop with their drill table - open up the top of the drill, it has 2 sets of pulleys, opposing each other like cones. Meaning - the smaller part (apex) of one cone aligns with the larger (base) of the other cone - this can be translated into high torque, low speed ratio or if the drive is opposite - low torque high speed ratio
The other is toroid gear technology - its used by nissans in japan in their bigger sedans, the toroid has a bearing face with the race gradually increasing in size - forming the same ratio variator
You cant control a CVT hydraulically with reliability thats why you have a separate TCU, furthermore the CVT will traditionally not use a torque convertor rather it has a slipping clutch inside the transmission to hold it steady at idle speed in gear (throttle or map/maf input will release the clutch to make the car go forward) - this is what screws up in the city CVT on CNG (the advancer messes the output of the map - forcing half the load to the drive belt which cant slip, and heating up the clutch as its trying to move the car but its actually stationary (no torque coming from engine)
controlling the transmission electronically is a great thing - this can make the transmission shift harder, quicker and not hunt - they are controlled by solenoids that when energized fill the fluid accumulators and move the shift pistons/brake bands into place to engage a ratio