If you follow Google's guidelines regularly, you may have noticed that they are really putting a strong emphasis on webmasters to make their sites mobile friendly. Some of the signs they sent out are:
- Publishing a testing tool to verify mobile friendliness
- Publish a set of mobile tutorials aimed at webmasters (including a specific one for Joomla)
- Sending out emails to owners of websites registered in Google Webmaster Tools that their site is not mobile friendly
- In mobile search results they actually indicate if a site is mobile friendly or not
However, the clearest sign was sent out by Google themselves, actually stating the following on the Google Webmaster's blog:
Starting April 21, we will be expanding our use of mobile-friendliness as a ranking signal.
All these are clear signs that mobile friendliness is becoming very important. Currently it is not yet a reason for a very clear SEO advantage in the rankings, but it seems that starting April 21 that will change. So, how can we make sure we comply?
Make your site responsive
Well, the first step is the most obvious. Of course you know if your current site is mobile or not. If not, change it. There are multiple approaches to this:
- A separate mobile site, someting like m.website.com versus the non-mobile version located at website.com
- Dynamic serving, offering HTML version based on the device
- Responsive design
Responsive design generally speaking is the advised solution, as consistent content is served from consistent URLs. Google published an extensive set of tutorials to help you set up your site:
Is Google able to see that your site IS mobile?
Now we come to something less obvious: even though your site is mobile, Google may not always be able to check that it is indeed mobile, and this may be your own fault. The problem is that many Joomla sites block Google's access to their CSS, and without any CSS, Google is not able to check that the site is mobile. Whether this issue applies to you is easy to check. You can use the Fetch as Google option in Google Webmaster Tools, but you can also do the Mobile Friendly test: at www.search.google.com/search-console/mobile-friendly. This test will show you whether your site is actually seen as mobile or not:

The solution is usually very easy if any issues are found: update your robots.txt and remove the lines blocking /templates and /media, see also this tutorial on my blog: Robots.txt: do not block CSS and Javascript. Note by the way that also Google Webmaster Tools allows you to check your mobile usability issues. Also W3C has recently published a mobile-friendly check (alpha).
Update: On March 11, Google announced the blocked resources report in their Webmaster Tools. This reports makes it even easier to discover resources that block correct rendering of your site by Google. Again a sign that the emphasis on mobile search is getting strong. Here is how the report could like like:

Try to get rid of any of these issues. Usually correcting your robots.txt file should solve these issues.
Mobile performance
Performance is also a very important issue. many users on 3G or even 4G don't experience the band-width they have at home, possibly making your site slow. Of course you should always take performance into account, but for mobile performance this is even more the case. Basically you should look at the reources you offer to users, especially as far as images are concerned. Especially images often make up the largest part of a site and are not that easy to cater for, but you can also look at excluding modules (like sliders!) for mobile views. Only offer users what they really need. There are some nice extensons that can really help you with that.
Just read the Mobile Performance section of the performance checklist on my site. It describes many options you have to enhance mobile performance.