You can reset your voicemail password through the automatic system by dialing *611 from your handset. The password will reset to 1+ the last four digits of your mobile number. Or you can conveniently login to My Verizon and follow these steps:
Go to Home Page
Select More Actions (This is highlighted in Blue towards the bottom of the page.)
Under Device select Change Voicemail Password
Select the option you desire: I will create my own password or Choose a password for me. Then click Submit.