I have found the easiest way to use Sublime with live HTML and CSS is to install WAMP(www.wampserver.com/en/) or XAMPP(www.apachefriends.org/en/xampp.html) which installs an Apache web server, PHP and Mysql server on your computer. Then you can edit your files in Sublime, and so long as they are located within the Apache web root folder (i believe its wamp/htdocs or xampp/htdocs) then you can go to localhost//filename.html and there is your html files. Save in Sublime and refresh the page and there are your changes.
You can also just open up the html file in Chrome or Firefox but selecting Open With... however, i have found that sometimes if you have dynamic content or links, they might not work correctly.
