If your carrier supports the iPhone voicemail feature, you can retrieve and listen to your voicemail right from within the “Phone” app and call your contacts back by simply tapping their messages. That type of functionality is pretty neat and useful, because it saves you actual time. If not supported by your carrier, you will not be able to see the visual overview of your voicemail inbox and use any of the related features. Tapping the “Voicemail” tab in your “Phone” app will simply call the number associated with your voicemail box. So let’s get going with creating our custom voicemail greeting on iPhone! How to record your own Voicemail on iPhone Phone → Voicemail → Greeting → Custom → Record → Save
Note: T-Mobile users, tap on "Keypad" or press 123. Verizon users, press *86 instead of 1. And Sprint users, press 1. And then you can change the default voicemail on iPhone from different carriers.

1. Open the Phone app — the app that you use to make phone calls and track your contacts — and tap "Voicemail" in the bottom-right corner.
When you receive a new voicemail, the Voicemail icon will appear in the notification bar. You can also access your voicemail to check your messages by selecting and holding the One (1) key from the dial pad, follow these steps: From any Home screen, tap Applications. Scroll to and tap Visual Voicemail. Scroll to and tap the voicemail message you want to hear. Tap the blue Play icon to listen to the message.