You send out your browser version and OS version everytime you visit a website. Javascript or something would figure out the resolution.
All the website has to do is check something called a useragent. Your useragent contains things like browser, os, and screen resolution. In php to get the browser you would use:
PHP:
get_browser(user_agent,return_array)
p.s. OMG!!! Power PCs are still around?!