To follow golf buddies tap the 'Search' icon (top-right) from the 'Feed' tab.
You can look for buddies by searching for their names and adding them from the suggested list. Just select the icon right next to the name and you'll be following this person.
Note: The 'Feed' tab is where the social activity of the Hole19 buddies that you follow will appear in conjunction with the personal activity that you share. Everyone who is following you will be able to see your activity in their 'Feed' screen and, in the same way, you'll be able to see the activity of the people you follow.