Mobile version of my site

I want to create a mobile version of my site:

http://isometricland.net/games/games.php

Basically, the only differences I want are that the far left column with my logo and social media links be omitted (or hidden?), and that the middle scrolling area fill the entire browser window.

I know how to generate the HTML markup and CSS, but how do I organize my site, and how do I get the server to detect the different browsers and feed them the correct version of my site?

Thanks.