I try to dial my voicemail to set it up, and it just gives me a busy tone. I've tried to reset my network settings, but nothing changed.
You have Visual Voicemail on your iPhone. To setup a greeting for it go into the phone app and click on the 4th icon at the bottom (voicemail). Then you should see where to record your greeting. If you have done all of this and it still isn't working then you may need to contact Verizon CS to make sure they have your account set up correctly.
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