Don't Post Pictures
Just like tickets that you buy for an event or a flight, you absolutely should not post pictures of your new Vaccine Certificate to Facebook or other social media. These items can be easily stolen just by taking a screen shot of your post. It's also a risk for identity theft - it shows your full name and date of birth.
The Vaccine Certificates became available for download on the 17th of November but as of this morning (the 18th) the site is still experiencing heavy traffic - you might want to wait until next week. You won't need it until the end of November at the earliest so there's no need to rush. The website is mycovidrecord.health.nz and you'll need a form of ID like your driver's license. You first create an account, then once you're logged in you can request your passport which will be sent to your email. When it arrives in your email you can upload it to your phone, print it, or just leave it sitting in your email if you want to. The key is to get it somewhere accessible for when you need to present it. The venue you're entering will scan the QR code and check your ID.