How does a microcontroller drive an LCD?
At some level a 320x240 display usually has 320 row drivers and 240 column drivers.  These drivers are almost always provided by chips integrated into the displays (often on flex PCBs around two edges of the display) with either a serial interface that supplies the data for one pixel at a time, or an intelligent controller with RAM to store the contents of the display.

The actual interface with a microcontroller ranges from 2 pins for i2c, 3-4 pins for SPI, 6-13 pins for a high level parallel interface to 30 or so pins for a pixel-by-pixel parallel interface.

OLED displays are basically the same although the interface between the driver chips and the display is different (same number of drivers required though).