Currently it is only possible to add Golf Clash friends using Facebook. Once your account has been connected to Facebook, any Facebook friends that play Golf Clash will automatically become your friend.
You can connect your account to Facebook via the in-game settings menu (Grey cog icon), by choosing the "Secure your account" option.
Once connected to Facebook, inviting friends in Golf Clash is easy. Simply select the News Hub menu (TV Icon) from the main menu screen and choose the "View All" option under the Free Coins section. You will then be able to invite your Facebook friends to play Golf Clash,