How do I add an Organic group to my main menu?
I love the new screeencast for OG, it explains it really well.

When you install OG it creates a few "views" that you can use. "OG list" view shows you a list of all the groups (you might have to enable the view if it's disabled). 

Then create your menu item "groups" and use "group-list" as the path. 

You can add specific "group nodes" to a sub-menu by editing the nodes and using the "provide menu link" feature. I believe not every theme uses submenus, for example Bartik doesn't by default.