Set up Messages on iPod touch
In the Messages app , you can send iMessage texts over Wi-Fi to people who use iPhone, iPad, iPod touch, or a Mac.
Sign in to iMessage
Go to Settings > Messages.
Turn on iMessage.
Sign in to iMessage on your Mac and other Apple devices using the same Apple ID
If you sign in to iMessage with the same Apple ID on all your devices, all the messages that you send and receive on iPod touch also appear on your other Apple devices. Send a message from whichever device is closest to you, or use Handoff to start a conversation on one device and continue it on another.
On your iPhone, iPad, or iPod touch, go to Settings > Messages, then turn on iMessage.
On your Mac, open Messages, then do one of the following:
If you’re signing in for the first time, enter your Apple ID and password, then click Sign In.
If you signed in before and want to use a different Apple ID, choose Messages > Preferences, click iMessage, then click Sign Out.
With Continuity, all the SMS/MMS messages you send and receive on your iPhone also appear on iPod touch. See the Apple Support article Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch.
Use Messages in iCloud
Go to Settings > [your name] > iCloud, then turn on Messages (if it’s not already turned on).
Every message you send and receive on your iPod touch is saved in iCloud. And, when you sign in with the same Apple ID on a new device that also has Messages in iCloud turned on, all your conversations show up there automatically.
Because your messages and any attachments are stored in iCloud, you may have more free space on your iPod touch when you need it. Message bubbles, whole conversations, and attachments you delete from iPod touch are also deleted from your other Apple devices (iOS 11.4, iPadOS 13, macOS 10.13.5, or later) where Messages in iCloud is turned on.
See the Apple Support article Use Messages in iCloud.
Note: Messages in iCloud uses iCloud storage. See Manage Apple ID and iCloud settings on iPod touch for information about iCloud storage.