Same as any other phone. call your voicemail press 9 enter your password and listen for directions from there.
Yea, same issue with me on Att network.. Frozen screen on voicemail settings. I was not even able to call myself to change the voicemail. I had to reset voicemail password over myatt app. And after that I was able to acess my voicemail over the phone. Still I cant change voicemail over the phone. Hope this will help you reset your voicemail.

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This article shows you how to save voicemail from iPhone, and export them as audio files to computer in the easiest way.