What additional components/boards are needed to use CAN with an STM32?
You should have at least two nodes and a twisted pair with 120 ohm terminations at each end. Identifiers must be unique. Read up on the various formats (11/29 bit) and CAN-FD vs. CAN. I suggest starting with 11 bits. The lower numbered identifier is the higher priority. 

Typically when a microcontroller supports CAN it means that the 2nd network layer (data link) is supported by a CAN MAC. Usually you have to supply a transceiver (the physical layer). CAN has (electrically) demanding requirements for maximum voltage tolerance that would typically be incompatible with low-cost monolithic processes that support microcontroller complexity. You can also buy chips with serial interfaces that implement the MAC, which you can connect to almost any microcontroller with (eg.) SPI. 

There are various high level protocols that can go above the 2 layers specified by CAN, or for a simple application you can implement your own. CAN messages are essentially broadcast and can be used or discarded by each node- like multicast or broadcast. 

A CAN protocol analyzer can be helpful- you can buy them for the value of an hour or two debugging.