Open the Phone app . Press and hold “1” to call your voicemail. Enter your PIN and press “#”. Press “*” for the menu. Press “4” to change settings. Press “1” to change your greeting. Follow the recorded instructions. How do I change my voicemail message? From the Home screen, tap the Phone icon . Tap Voicemail then tap Greeting (upper-left). Greeting is located in the top-left corner of screen. Tap Custom to record a greeting. Enabled when a checkmark is present. Tap Record to begin recording the custom greeting message. Tap Stop to end recording then tap Save. Call *86 (*VM) from the handset or the 10-digit mobile number from another phone. Follow the instructions for choosing the language options then press the # key to confirm the choice. When prompted, enter the 4-7digit password then press the # key. When prompted, say the signature (or name) then press the # key. Open your Android’s Phone app. It usually looks like a phone receiver at the bottom of the home screen. Press and hold the 1 key on the keypad. Tap Add number. Tap Service. Tap My carrier. Tap Setup. Tap Voicemail number. Type your mobile phone number and tap OK.
How to set up the voicemail greeting for your phone extension / direct phone number with Telzio. 0:26 - How to set up your voicemail greeting directly on you

For personal users, a funny iPhone voicemail message may be just what you want. It’s still a good idea to keep it short, but you can have some fun by using your iPhone to record a funny voicemail message played over a speaker on your computer or another device.
Just click the "Phone" App from the home screen of iPhone. You can press "1" or the "Voicemail" key to access to voicemail on AT&T phone. 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.