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
Read more about stopping your answerphone kicking in too quickly here: How to stop my iPhone going to voicemail after three rings

Great question! Although I don’t know if there is a specific function for this on your particular phone, the best way to save the message is the simplest. Turn up the sound as high as you can and record it onto a digital recorder (like you would use for a lecture), a cassette recorder or your cell phone if you have a voice recorder on it. Then save it as an MP3 on to your computer for safe keeping. You can also Google your vtech model number to see if you can find an owner’s manual. They might have a way to save a recording in there. Probably not, but it’s worth a shot.
To force close Phone, on iPhone X and later swipe up until you see the apps in task view, then swipe up again on Phone. On iPhone 8 and earlier double press the home button, then swipe up on Phone. You will see all the open app cards.