With Verizon's stock email app, you can't. You can listen to your VM messages on your phone by dialing *86, or from any phone by dialing your 10-digit phone number and then pressing the # key while your greeting is playing.
To hear your messages online you need to have a third party app on your phone. You posted this in the Apple section, so if your phone is an iPhone, you'd need to go to the iTunes store and find an email app that will give you web access to your messages.
An alternative is You Mail - a free service that works with any phone number. I've used it for several years and it's a great service, and free!!
You might could by having a VOIP program on your computer and calling your phone number from your computer that way. IDK.