How do I block my number on phone calls?

From the home screen, tap the "hamburger" icon in the upper left. (Or swipe from the left side of your screen on any screen.) Then tap "Settings" and toggle "Block Caller ID" on.

Now, when you make a phone call via the app, your number will not visible to the person you're calling. The person you're calling will see something like "Unknown Caller" listed for the incoming call.

Alternately, if you use an Android device, you can display a Google Voice number instead of your personal number.