Typology uses the standard WordPress menu system for navigation. To set up your menus, go to Appearance -> Menus. Please note that some items (i.e. posts) are hidden by default in the screen options so make sure you check it.
Main navigation menu
You simply need to create your menu and add items you want to show. After the menu is created, you need to assign this menu to the Main Menu theme location, as described on the image below.
Watch the process in this short video:
Social menu
As shown in the image below, this is a menu where you should put custom links to your social profiles. Note that you just need to specify the link to your social page i.e. http://facebook.com/link-to-your-page and the Facebook icon will be automatically recognized.
Watch the process in this short video:
If you are not familiar with using WordPress menus and its basic setup, there is a great user guide on the official WordPress Codex.