You need to subscribe to the Visual Voicemail from Verizon Wireless, I believe.
There might also be some third party applications available.
I believe the email feature from within Visual Voicemail is model-specifc. You may want to call customer service and make sure that feature is available on your specific phone model.
Some models allow saving the file that Visual Voicemail receives to local storage (e.g., SD card). If your model can do that, you may be able to use one of the mail apps to attach it.