How do they predict an earthquake?

It will be better if you have defined whom you are referring when you are saying "they". But taking it on a broader view below points can be of help:

1. Laser beams can be used to detect plate movement.
2. A seismometer is used to pick up the vibrations in the Earth's crust. An increase in vibrations may indicate a possible earthquake.
3. Radon gas escapes from cracks in the Earth's crust.