You will be asked to delete your current Voicemail greeting. Click on the ‘Yes’ button that appears on the screen if you want to remove that. You can save your new recorded Voicemail greeting or can use the default recorded option. Wait and hear the new Voicemail greeting message that the instructions speak out. If you want to keep that recording as your Voicemail greeting, then save it. Or you can re-record the message to get a different greeting.
Open your device’s Phone app ​.At the top right, tap More .Tap Settings. Voicemail.You can: Change what handles your voicemails: Tap Advanced Service. Set up your voice mailbox: Tap Advanced Setup. Change your notification settings: Tap Notifications.

The default voicemail greeting on the iPhone plays generic Your call has been forward to an automated voice message system recording. If you use your phone for work, create a personalized greeting that tells people you're a professional. If your phone is for personal use, create a personalized greeting so people hear your voice and know they called the right number.
To check your voicemail messages from another phone: Call your 10-digit wireless number. When you hear your voicemail greeting, press the * key to interrupt it. If you reach the main voicemail system greeting, enter your 10-digit wireless phone number, then interrupt your greeting by pressing the * key. Enter your voicemail password when prompted.