The fastest way to learn MEAN stack is by learning each individual technology in the MEAN stack. Learning MongoDB, Angular, ExpressJS and NodeJS is quite easy, the difficulty is incorporating them into a single application so that they can work with each other. So you should first follow online tutorials that teach you how to use these technologies. then try to use them together with each other.
You can read this blog that explains what MEAN stack is.
Learn full stack web development in detail by signing up for this professional Full Stack Training offered by Intellipaat.
You can also get started with MEAN stack by learning individual technologies, like:
If you wish to learn MongoDB you can do this end to end certification course on MongoDB.
Also you can learn Angular by doing this Angular course
or you can watch small tutorials to get your feet wet on MongoDB, Angular etc,