Some Joomla templates support mobile devices. It's the easiest way to create a mobile template for Joomla.
But if you built a template, you
can use some extension to present your website on various mobile device
types. Mobile Joomla might be one of the first plug-ins recommendations.
You can read this article to know more about Joomla mobile solution.
For concepts of mobile template, read this article may be helpful for you, too.