You need to make sure that your carrier supports Visual Voicemail first. If they do, they will turn it on for you. Voicemail is a carrier function, and they need to activate it. Once they do, it will have a password set, they would tell you what it is. Then you can go to Settings>Phone, and you can change the password to something you know. After that, all you have to do is tap on the Voicemail button and it should open.
Visual Voicemail instructions for IPhone 5s.
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Does IPhone 5s get Visual Voicemail