You can put these things one after the another to get more complex behavior.
Roughly speaking, common collector/common drain amplifiers have a gain of approximately 1, but has low output impedance, which makes it suitable for driving big loads (like the outside world). Common emitter/common source amplifiers have high output impedance but tons of gain.
The classic op-amp topology is a differential amplifier (long-tailed pair, in the wikipedia template) feeding into a common emitter/source gain stage, then into a common collector/drain follower output stage.
To answer your last question, the output of the gain stage is the drain of the transistor, that feeds the gate of the common drain output stage transistor.
The gate is usually the input terminal, but sometimes the gate is at a fixed voltage and the drain is the input terminal (cascode-y circuits are like this, aka common base or common gate).
For the tree transistor horsemen (BJTs, MOSFETs, JFETs), they can all be fitted into similar transistor amplifier building blocks:
https://en.wikipedia.org/wiki/Template:Transistor_amplifiers
You can put these things one after the another to get more complex behavior.
Roughly speaking, common collector/common drain amplifiers have a gain of approximately 1, but has low output impedance, which makes it suitable for driving big loads (like the outside world). Common emitter/common source amplifiers have high output impedance but tons of gain.
The classic op-amp topology is a differential amplifier (long-tailed pair, in the wikipedia template) feeding into a common emitter/source gain stage, then into a common collector/drain follower output stage.
To answer your last question, the output of the gain stage is the drain of the transistor, that feeds the gate of the common drain output stage transistor.
The gate is usually the input terminal, but sometimes the gate is at a fixed voltage and the drain is the input terminal (cascode-y circuits are like this, aka common base or common gate).