The offer is for a new Mac (or iPhone, iPad, iPod touch, Apple TV box) from Apple or Apple Authorized Resellers.
The offer is for new subscribers. One offer per customer. Current or previous subscribers may get excluded to redeem in the automated procedure.
For Macs, additionally sign in to the TV app (menu Account), or you may not get to see the redeem button.
To redeem, find the “Enjoy 1 Year Free” button the the TV app.
Read here how to redeem: Apple TV+ - One Year Offer - Apple
Read here about the conditions: Apple TV+ one year offer - Terms and conditions - Apple
Read here if you have trouble redeeming: If you can't redeem your promotional trial of Apple TV+ - Apple Support
↳ Last step is to contact Apple Support for assistance, if needed.