The most common causes of a vehicle to shake while at idle is due to engine misfires causing the engine to vibrate which results in the vehicle shaking.
Engine misfires could be caused by bad spark plugs, loose spark plugs, low fuel pressure, bad ignition coils, bad spark plug wires and even the throttle position sensor could cause an engine to misfire if the engines computer doesn't know exactly where your vehicles throttle is located and then doesn't know the amount of fuel to send to the vehicles engine.
An engine that gets too much fuel can flood the engine causing it to misfire.
Another cause of an engine shaking the car while idling is bad or failing engine mount.
The engine mounts reduce vibration from the engine to the vehicles frame so if the rubber is going bad or missing from the vehicles engine mount then the engine could vibrate and shake the car at idle.