With many websites receiving the majority of their traffic through mobile devices or tablets, it is vital that your site is designed and programmed in such a way that that ensures everything works and displays exactly as it should. It is not acceptable to simply just shrink every element on the page to fit on a mobile device as often when doing this, you make some elements too small to read or to be able to click. In the eyes of the search engine, this means the site is not compatible for mobiles.
Often you may take the navigation off the page and put in as a separate flyout menu. Sometimes it is worth not displaying certain banners or elements on mobile devices as they simply will not work. This can be fairly straightforward to do.
Before setting a new site live or even if your site is already live, it is vital that you test it on a number of different devices using different operating systems and screen sizes as this can alter the appearance quite a bit and you may need to change some of the code in order to get it working correctly on as many if not all devices as possible.