The information is thanks to fellow Microsoft MVP Darrell Webster and his original blog post on the topic here:
I’ve been busting to get a look at Office 365 Planner. I know it has now become available and that I need to have First Release enabled for my whole tenant turned. However, I still hadn’t seen it appear. Then along came Darrell’s blog post to the rescue.
The first step to enable Office 365 Planner Preview is to open a new browser using in-private or incognito mode. This will ensure that you don’t automatically log into an existing tenant because we want to all the Planner Preview to an existing Office 365 tenant.
In this new browser window navigate to:
You should see the page above displayed. In the top right corner select the Sign In option to add Planner to an existing tenant.
You should be then taken to the familiar Office 365 login page as shown above. Login here as a global administrator.
You’ll then be asked to confirm adding Planner to this tenant. Select the Try now button to continue.
You’ll then be given a summary of the order. Select the Continue button.
This will then complete the process and take you to the Office 365 admin center.
It is unlikely that the planner tile will appear immediately in your Office 365 app launcher as shown above. It may take up to 24 hours for this to appear.
You’ll need to then go into the users you want to give access to Office 365 Planner and assign them a license as shown above.
Until the tile appears you can access Office 365 Planner directly using:
You might need to login as a valid Office 365 user that is licensed for Planner. If all is good you should see the above screen and you are now ready, like me finally, to start using Office 365 Planner.
Once again, thanks to Darrell Webster for taking the time to document this.
More information about Planner once I’ve had a play.