A well developed website should work well on all devices. However the mobile platform presents specific challenges such as bandwidth and browser size. One option is to build a dedicated mobile version of your website, but you would then need to update your content on two sites. Here are two alternative solutions for mobile-friendly Joomla sites.
Some templates are now being coded so they work well in both desktop browsers and mobile devices. A great example of this is the CloudBase template by CloudAccess. This template is already very flexible with a wide range of module positions and parameters. The mobile template is displayed automatically whenever someone visits the site using a mobile device, but if they prefer, they can switch to the normal layout.
There are a few extensions available that create a mobile compatible version of your Joomla site. I installed Mobile Joomla! on a standard Joomla site and tested it on a smart phone. It worked very well without any configuration. There is a bit of work required if you want to include your modules, but there is good documentation on the website.