How to reset voicemail on my iPhone?

How does one reset the voicemail whenever it doesn't show the "greeting" nor the new messages - I have to "call Voicemail" and then enter a password for it to retrieve messages and I would like to "SEE" the messages but don't. It doesn't show me what messages have been saved and I'd really like to be able to SEE these again

[Re-Titled by Moderator]