Setting up you 2nd WordPress Site

I need some advice, because I'm not finding a clear answer. I already have one WordPress site which is hosted on Bluehost, but how do I set up a 2nd WordPress site? I need the site to use a different theme. The two site will be different in many ways, but will share some core components as well. Can a fresh install of WordPress be installed on a subdomain, or are there better solutions? I appreciate any help you may provide.