Hello,

There are several reason why the car vibrates at idle. You could have a vacuum leak, it can also be an issue with misfire that is only noticeable at idle. Could be an issue with mass air flow sensor.

Rough idle can also trigger the check engine light, if its due to misfire or a sensor. Is your engine light illuminated?

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

First do a visual inspection under the hood and look for any cracked/broken or un plugged vacuum hose. You can also check for leak on the intake manifold by spraying carb cleaner which can indicate if there is a leak.
Here is a helpful guide:

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

A dirty mass air flow sensor can make the vehicle run rough as well. Many times servicing the sensor by cleaning it can fix the issue.

https://www.2carpros.com/articles/mass-air-flow-service

Also the engine might need a tune to restore smooth idle. By changing spark plugs, air filters, fuel filters etc.

Here is a guide to basic tune up:
https://www.2carpros.com/articles/how-to-tune-up-a-car-engine

Please let me know of any questions.
Thank you.