What I did was open the My Verizon app (you can get it from the Play Store if you don't already have it) and log into your VZW account.
Once you're in, pull out the left side meny and tap Account, then tapp Add-Ons. Select the line you want to have VVM on.
Move to the Essential Services section. This is where the VVM options are. Now, I opted for Premium because I like the text transcription, but Basic VVM is an option as well. If you tap View, it should explain the service and give you the option to add it to your account. There are a couple confirmation steps and that really should be all you need to do. It might take 10-15 minutes to activate and appear on the account.
Once I did that, I went to my Phone app, went to Settings, selected Calls, and tapped Voicemail. Toggle the switch to turn Visual Voicemail on and it worked for me. The 4th menu showed up in my app and was good to go.
If things continue to be wonky for you, I'd call them and see if they can help you through. It worked pretty seamlessly for me when I activated it.
Hope that helps.