In the Messages app > 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 Manage Apple ID settings on iPod touch for information about iCloud storage.