If you are using a IP 400 series desk phone, press the Voicemail function key. If you are using a Cisco 7900 series desk phone, press the "Messages" button (envelope icon). If you are calling from a phone other than your own desk phone, dial your own phone number and press the * key when you hear the voicemail greeting.
2. 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.

This solution worked for me: https://www.reddit.com/r/apple/comments/3lm2eh/difficulty_changing_voicemail_gre eting_in_ios_9/cyngnjr
After setting the number on your voicemail, you must also record a personal voicemail greeting. Follow the steps below. Start the Phone app. if you don’t see the numeric keypad, tap “Keypad” at the bottom of the screen. Tap and hold the “1” for about two seconds until the phone automatically calls voicemail. Immediately tap “3” to access voicemail settings. Listen to the options. On most voicemail systems, tap “2” to start the process to record a new greeting. The current personal greeting will play; then tap “2” again to record a new greeting. Say the greeting you want, and tap “#” when you’re done. To save the greeting, tap “1.” The personal voicemail greeting has been set. Hangup the phone. How to setup voicemail using a Visual Voicemail Applications