Note: If necessary, delete an existing greeting (limit of 2 greetings) to make room for the new greeting: Tap the Menu key, tap Delete greetings, tap the check box next to the desired greeting, and then tap Delete. Tap the Record icon to record your greeting. Tap the Stop recording icon to stop recording.
I got a new cell phone recently. As the world stood in line to pick up the latest iPhone 8, I graduated to the 6S. I pride myself on that actually. As with all new phones in the 21st century, the voicemail must be set up anew. I used the default message for the first few days, but finally settled down to record a more personal greeting.

Make sure that you set up your voicemail. To check, dial your own phone number from your iPhone and leave yourself a message. Call your iPhone from another phone and try to leave yourself a voicemail. Go to the keypad and press and hold on the 1, or press the Call Voicemail button. This dials voicemail. Check if you have any missed messages.
“Hi, you’ve reached [your name]. I’m away from[date] to [date]. If you need help with [X] before then, please contact [name] at [phone number]. Everyone else, please leave your name and number and I’ll return your call when I return. Thanks and have a great day.” “Hello, you’ve reached [your name]. I’m currently [exploring Asia, hiking through the jungle in Costa Rica, hanging out on the beach in Bermuda] — or more likely, [recovering from extreme jet lag, googling ‘Are red spiders poisonous,’ or looking for SPF 150 sunscreen] and won’t be back in the office until [date]. Leave your contact info and reason for calling and I’ll get in touch then.” “Hey there, this is [your name] from [your company]. I’m out of the office until [date]. In the meantime, please direct your inquiries to [coworker’s name] at [email address]. [He, she] can also be reached at [phone number]. Thank you.”