You can play with your Facebook friends, so make sure both you and your friends have accounts connected to Facebook. To link your Golf Rival profile to your Facebook account, go to Menu → Settings → Protect your account → Facebook.

To play with a Facebook friend, tap the blue "Play with Friends" button under the "PLAY" on a Stage. There, you can select the friend you would like to play with and send them an invite. When they accept it, the match will start!

Friends are also useful, as you can send gifts and coins to each other. To see how, check out How do I send gifts to other players?