Most paintguns use simple microswitches as their trigger.
These tend to be cheap, reliable, and provide a bit of tactile feedback when they're pulled.
A bit more rare are optical switches, which is an arrangement, of two parts: a small light emitter and an electronic "eye" that tries to see the light. When a part of the trigger passes through them the "eye" detects that the beam is light is broken and tells the circuit board to fire the gun. Optical triggers can theoretically be softer and shorter than microswitch triggers, but they're a bit "mushy" by comparison and offer no tactile feedback.
Those are by far the two most common types of electronic triggers, but there are a couple others out there. The old BE Rainmaker used a pushbutton trigger switch and I've heard of people custom installing piezoelectric and magnetic switches in guns.