*67 if you want the option to block your number on a per call basis.
If you want to permanently block your number so you don't have to enter *67 everytime:
1. Sign-in to My Verizon.
2. Click on the My Plan tab.
3. Click on Add/change features.
4. Check the box near "Caller ID Blocking."
5. Click the Next button at the bottom of the form.
Some Android phones have the option built into the phone... others do not.