How to use components that don't have a shield?
Your observation is correct. Everything breaks down to some number of physical connections and some protocol for communicating with the device. Shields and libraries associated with them do most of the work for you, but not everything comes in a shield.

There are some common protocols for interfacing with devices, including SPI and I2C. From a quick peek at the driver interface sheet, it looks like they're using SPI. Well, your Arduino already supports that so you can hit the ground running with this display. You just need to know what commands to send to it, which you can find from the display's datasheet.

Note: It looks like the 2" screen requires 3.3V while the 7" one supports up to 7V.