If you are going to use Wordpress to manage your new subdomain, you'll need to install it just like you installed Wordpress into your primary domain.
The installation of Wordpress in your new subdomain is completely separate from the one in your primary domain. You will need to configure your new dashboard, choose whatever theme you'd like, install any plugins you might need.
Once you have created a subdomain site, you'll need to provide links back and forth between your primary domain and your subdomain site. (Wordpress help page on menus.)
Different themes allow different theme options, so it's impossible to give instructions that will apply to any possible site you might set up in Wordpress. These instructions are for the default theme, though these instructions should apply to most any theme you might choose.
By default, if you don't do anything to manage the menu on your site, every time you create a page, it will automatically be added to your navigation bar and sorted alphabetically. Pretty much every Wordpress theme allows you to create at least one custom menu for the site, many of them will allow more than one. The default theme allows you to create 2 different menus–the top primary menu and a secondary menu in the left sidebar.
Once you have created your first menu, you'll have a new tab appear, Manage Locations.
To add a link in the navigation menu back to your primary domain, which means I need to add a link.