How is vibration isolation achieved in helicopters?
There are many techniques.

Passive reduction techniques involve designing the powerplant, transmission, gearbox and particularly the rotor(s) to minimize vibration. Designers carefully arrange all the moving parts to be as closely balanced as possible. They can be mounted using flexible parts and springs to damp vibrations (the same principle behind the shock absorbers in an automobile). The sophistication of helicopter design has evolved over time as engineers learn more about the characteristics of helicopters and how mechanical parts behave. Computer-assisted design has also allowed for huge improvements here as moving parts can be simulated in great detail to optimize each individual part for minimum vibration.

Active systems work by using accelerometers to sense the vibration of the helicopter at certain points in real time. This data is then used to shake a reaction mass back and forth to create vibration opposite to that of the rest of the helicopter. The two opposite vibrations cancel each other out. Effectively, the active system is using electrical power to dump all of the vibration energy in the helicopter into a small mass, so the helicopter stays still while the reaction mass in the active system shakes to absorb the energy. Such systems are already in common use in large transport helicopters and are becoming more prevalent in smaller helicopters as well.