Note: a desk phones' voicemail greeting can only be recorded via phone, there is no way to upload or download a greeting through the online panel.
When you get a voicemail, you can check your message from the notification on your phone. Swipe down from the top of the screen. Tap Voicemail ….You can call your voicemail service to check your messages. Open your device’s Phone app . At the bottom, tap Dialpad . Touch and hold 1. How do you listen to your voicemail from a different 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. Can I listen to my voicemail without setting it up?

I called into my voicemail, and tried to change the greeting to no avail. After a few attempts, I realized that I had had an "extended absence" greeting in effect. Once I switched to a "custom" greeting, I was able to record and activate a custom greeting.
If you don't record a new greeting, callers hear the default greeting. To record a new greeting: Open the Google Voice app . At the top left, tap Menu Settings. In the Voicemail section, tap Voicemail greeting. Tap Record a greeting. Tap Record . Record your greeting and when you’re done, tap Stop . Choose what you want to do with the recording: