Creating a mobile site/stylesheet with existing Child theme?

Hi,

I’ve been researching making a responsive mobile site, but I was wondering what the best way to implement it would be given I created a child theme for Twenty Ten. The site (https://www.caitlintighe.com) currently displays without any change when viewed on a mobile device. I’d rather come up with some way for me to just write code altering the layout, with it still inheriting the child theme’s text styling and such.

So what is currently the best way to do this? Are there any plugins that support a mobile site using a child theme, or is there a way I can create a separate mobile stylesheet to be included with the child theme?

Thanks in advance for your help!