What could make a car start idle and shake and then it turn off?

This could be the IAC motor, vacuum leak, bad spider injector, weak fuel pump. bad PCM for starters. Let's start by running the codes this guide can help:

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

Will it run on starting fluid? This can tell you if the fuel pump is bad or a bad spider injector.

https://www.2carpros.com/articles/car-not-running-advanced

Please go over these guides and report back.