So, I am very familiar with the 737NG, and there is a trim switch on the yoke for vertical trim. However, I can't seem to locate this trim switch in the A320. Is there a trim switch on the joystick in an A320? If not, how do they trim?
The pilots do not manually trim an Airbus in pitch. The flight control computers provide automatic trim:
The normal-law flight mode is a load-factor-demand mode with automatic trim and protection throughout the flight envelope.
Following normal law, the sidestick controllers set the elevators and THS to maintain load factor proportional to stick deflection and independent of speed.
With the sidestick at neutral, wings level, the system maintains 1 g in pitch (corrected for pitch attitude), and there is no need for the pilot to trim by changing speed or configuration. Pitch trim is automatic both in manual mode and when the autopilot is engaged.
(A320 FCOM - Flight Controls - Description - Normal Law - Flight Mode)
There is however a mechanical backup:
The pilots use mechanically interconnected handwheels on each side of the center pedestal to control the trimmable horizontal stabilizer.
(A320 FCOM - Flight Controls - Description - Cockpit controls)
You can see the full flight control logic in the following image. The pitch trim is indicated by THS (Trimmable Horizontal Stabilizer):
(image source: A320 FCOM - Flight Controls)
Autotrim :D or Manual trim by moving the trim wheel. Trim wheel has priority over Autotrim. But if you move the wheel with AP on, it will disengage. Also AP doesn't need to be on for Autotrim to work. It's always working in normal and alternate law, until bank angle of 33 Deg, then you are on your own.