If your phone has Visual Voice Mail, you can do exactly that.
Otherwise, you would have to contact VZW to get the the number to CBW, which is their Voicemail archival service.
the website that you would have to visit for the archival process of the voicemail would be www.cbwproductions.com/vwclientsorder.html
Its $5.00 per .mp3 file emailed to you