Modern Webdesign has to take into account that web surfers use new devices: smartphones and tablets. Visitors of your domain go online in different situations (for instance during their subway trip) and with different interests than in the office. Responsive Design is therefore not only a technical issue but a conceptional issue as well.
Needed are designs for at least 3 devices (notebook, tablet, smartphone, eventually big monitors). CSS-Media queries help to adapt the layout to various screen width and qualities. Taken into account as well is the usability of the site on touchscreens and the performance of the site in situations of bad connectivity. This means for example smaller image files on smartphones. Flash animations do not work on smartphones.
In preparation on responsive design you should have a look at the statistics of your website: What kind of devices use your site's visitors? Which are the themes they are interested in mostly?
There are many templates/themes for cms like Joomla! or Wordpress in responsive design, that can be adapted to your needs.
A better performance of your site is caused by an own template.
We implement responsive designs to all kinds of websites - ordinary coded HTML-sites, too.