AT&T: If you’re an AT&T customer, you have the option of creating your own basic voicemail. You’ll need to press and hold the 1 key down while you’re on your phone. AT&T will then ask you to set up your greeting via voice prompts.
To set up voice mail, tap the Phone icon, tap the Voicemail icon and then "Greeting.". There are two options available: Default and Custom. If voice mail hasn't been set up previously on your phone, Default is selected, which means people will hear your wireless carrier's generic voice mail greeting when they call you.

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.
4. When you're ready to begin recording, tap on "Record" and begin speaking. Once you begin recording, you'll see the line turn red. This indicates how much time you have left.