Hello,
well first of all you need new template files, after that if template is for same version of Joomla that you have, you can do just simple file overwrite. New template will add necessary files and customization for responsiveness.
If responsive template is for newer version of Joomla that you don't have. You'll need to update Joomla first, but make sure you baked up your files, customizations and also that all of yours modules and plugins are compatible with new version of Joomla.