For Spotify Premium members, simply log-in and follow the prompts. If you've previously received a free Google Home Mini from Spotify through an older offer, you won't be able to get another for free this time. I'm not a Spotify Premium member, so I can't really speak much more on this.
For Google Fi customers, simply launch the Fi app from your phone and there will be a banner at the top where you can redeem your freebie.
Now I am a Google Fi customer, so I was able to snag this. After you click the redeem link, you'll be taken to the Google Store checkout page. Select your Google Nest Mini color of choice and shipping address and you're all set! My $50 freebie should arrive in about 2 weeks 🙂