Today, John Mueller (Webmaster Trends Analyst at Google) confirmed and tweeted:

FYI The mobile changes mentioned here are now fully rolled out. https://t.co/fTB3ia6LJ2

— John Mueller (@JohnMu) May 12, 2016

 

Last year,  Google started using mobile-friendliness as a ranking signal on mobile searches.  In March 2016 Google announced that beginning in May, Google will start rolling out an update to mobile search results that increases the effect of the ranking signal to help the users find even more pages that are relevant and mobile-friendly.

 

 

There are many resources shared by Google online to check and test the mobile-friendliness of a website are as follows:

• If you want to find out if a page is mobile friendly then take the Mobile-Friendly Test
• If you want to make a site mobile-friendly with a 3^rd party software then see Customize your website software for mobile users
• If you want to dive into technical details then Review the Getting Started section on Web Fundamentals, our resource for web developers
• you can use your Webmaster Tools account to get a full list of mobile usability issues across your site using the Mobile Usability Report.
• Read the Mobile SEO guide for an overview of
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  the implementation process

Some Other Google Resources answering the following questions:

1. Why make a website mobile-friendly?
2. How do I start?
3. What are the top three things I should know when building a site for mobile devices?
4. How much does it cost to build a site for mobile devices?
5. What should I think about when working with a developer?
6. What are the top three mistakes beginners want to avoid?
7. What are the next steps?