A common question I see is once I go through the effort of making my site mobile friendly for Google's mobile friendly algorithm, how long will it take Google to notice the change and rank my web pages accordingly?
I tested this a few times and it really depends on how much content on the site changes on a regular basis. It can range from as soon as a few hours to well over 72-hours for all your pages. There are some tricks to speed up the process, which I will explain below.
On Friday, I changed over a very static site that is rarely updated from being non-mobile friendly to being mobile friendly. As soon as the new site was live, I first tested it in the mobile friendly testing tool and it validated. Then I used Google's Fetch and Render tool in Google Webmaster Tools to resubmit the top pages of the site to Google, so they can fetch those changes sooner than the less important pages. I also submitted an XML sitemap file with the change date in the file as being the date the new mobile friendly pages were updated and submitted the sitemap via Google Webmaster Tools. Those are some of the better eways to expedite the mobile update.
As of today, those most important pages were indexed and by Saturday (less than 24 hours) were showing as mobile friendly in the Google search results. Still, many of the older less important pages are not yet showing the mobile friendly label in the search results.
A WebmasterWorld thread has others with the same experience. Some say it took them as less than 12 hours and some said over 72 hours. I'd expect really massive sites to take up to a month or longer, it just depends on the freshness of all your pages, the size of your site and how much Google wants to crawl you.
Forum discussion at WebmasterWorld.