Coming from a stop your car shakes when the clutch pedal is release.
Car Problem Diagnosis
This kind of problem cannot be easily detected not unless a thorough inspection of a qualified mechanic on your car drive train is conducted. However, the following are the possible cause of this kind of problem.
Possible Cause of Car Shakes when Clutch Pedal is Release
Loose engine or transmission bolts or a faulty clutch disc.
Loose engine or transmission bolts because engine or transmission bolts is the one that keep the engine and transmission to be connected and become stable, thus if one or more bolts are loose the transmission assembly will vibrate and become noticeable especially when the clutch was engage from a stop.
Faulty clutch disc, clutch disc is the one that pressed against a flywheel to allow the transfer of engine power into the transmission. When the clutch is faulty it will have an even contact with the flywheel thus a vibration will occur.
All About Auto Recommendation
You do not have much of a choice than to bring your vehicle to a reputable auto repair shop and have a mechanic inspect the clutch and transmission assembly, this will be very costly.