Do helicopters have trim? How does it work?
It depends on what you mean by trim. 

If you mean a a mechanism that allows the pilot to reduce the control forces in order to allow the helicopter to be flown hands off, then the answer is a qualified yes. 

If you mean a trim tab attached to a control surface, then the answer is no. Many airplanes which have a trim control do not use a trim tab. For example, Pipers have an anti-servo tab on the elevator, which the pilot uses to reduce control forces. 

 

Since helicopters are unstable -- meaning if you take your hand off the cyclic the aircraft will be in an unusual attitude within a second -- nothing short of electronics and actuators will allow a heli to be flown hands off. 

But every heli except the smallest ones, have considerable stick forces, which make them difficult to impossible to handle without some kind of assistance.  

The simplest setup is what you find on the original 4-seat R-44 Astro, which lacked hydraulic assist. On top of the cyclic you will find a 4-way "hat" switch which uses electrical actuators on the cyclic to reduce the control forces necessary to fly it. 



Larger helicopters have hydraulic assist, which allows the copter to be controlled with just two fingers. Inop hydraulics is considered an emergency. 



Big helicopters have a stability augmentation system, which allows the helicopter to be flown hands off. An SAS is required for IFR flight.