While a $10 per month Basic subscription is available, you'll need to drop a little more cash to get the Google Home. With All Access, subscribers will also get the NYT Crossword, NYTimes Cooking, and a free subscription to give to someone else. Google Home retails at $130, so this option (which comes up to $204 for twelve months) is a pretty solid offer if you already want the NYT daily. The Home Delivery option gives you all of the above, plus an actual paper edition delivered to your home daily, along with some extra behind-the-scenes content and special print-only features like The New York Times for Kids and dedicated crossword sections. You'll get two All Access subscriptions to give away, too.
The Google Home offer is only available until December 31st of this year (or when supplies run out). When you pay for the subscription option, you'll get a code that can be redeemed at the Google store; it must be redeemed by March 18th, 2018.
Update: As noted by The Verge, it seems that the NYT has pulled the offer already after several people signed up, got a Google Home code, then canceled their subscription after paying only $17 for the first month of service. (h/t Joshua Allen)