What is the best and most quick way to remove popcorn drywall from a ceiling

How old is the textured ceiling, and do you know if it contains asbestos?

You plaster over it.

As talaniman said, make sure this is not a popcorn with asbestos in it and then you plastic off the area (floor/walls), wet the ceiling and then use a scraper or trowel to scrape the popcorn off...should be that simple!

Click on the videos below for some more ideas:

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They sell a large pole scraper at home depot...might speed removal for you.

Good luck!

Mark