Automatic transmissions have way too many moving parts making them very difficult to comprehend. So I went ahead and simplified it a bit to get a basic understanding of how it all works in a traditional, torque converter-based system.
Your engine connects to your transmission at the bell housing. The bell housing contains a torque converter for automatic transmission-equipped vehicles unlike a manual transmission were they meet at the clutch. The torque converter is a fluid coupling whose sole purpose is to connect your engine to your transmission and eventually to your wheels. The transmission contains planetary gearsets which provides different gear ratios.
A lot more is going on when driving a manual than what was showed in Fast and The Furious when they’re driving those 20 gear cars (hollywood shifting joke). I’ve always wanted a step by step on what is really going on. So I found this very helpful in some questions I had about a manual gearbox.