Only way I'm aware of is by using a service that Verizon contracts with; it's pricey ... go to this link:
and scroll toward the bottom under Voice Mail Archival.
Also, this won't help with current voice-mail messages, but someone on another thread the other day indicated that youmail may let you do this. You have to sign up for the service at youmail.com. I don't know if it works with basic phones or not, but you might want to check it out.
You also could try playing the voice mail(s) over your speaker phone and record them onto a tape recorder (if you have one) or onto your computer via its sound recorder.