A personal voicemail greeting is an easy way to prevent callers from hearing a generic greeting message. It ensures that people know they've reached the correct person, and makes them feel more comfortable leaving a voicemail. To change your voicemail greeting on an iPhone, you'll need to follow a few simple steps.
Once you enter the password of Voicemail, you can tap on "Done" button. Next, you have to type in your password again. Finally, tap on "Done" to finish password setup. Now Press and hold the number 1 from your phone to access voicemail. Part 2: How to Change and Record your Voicemail Greetings on iPhone

Android phones can access voicemail by holding down the 1 key on the dial pad until the phone dials your 10-digit phone number. You will automatically connect to your mailbox and be prompted to enter your temporary password; this password is the last 4 digits of your phone number followed by the # key. Start the Google Voice app. Tap the three horizontal lines at the top left of the screen (sometimes called a hamburger menu), and then tap “Settings.” In the Voicemail section, tap “Voicemail greeting.” Tap “Record a greeting.” How do I access my voicemail? To call your voicemail on an Android phone, simply open your phone’s dial pad and hold your finger down on the “1” key. You can also call your voicemail from a different phone by calling your own number and tapping the pound key. How do you check your voicemail?
Once you have your new iPhone in hand and you are learning how to use it, one of the first things you may want to do is record a voicemail greeting. You have the option of using a default one that tells the person what number they have called, but you may elect for a more personal option.