Once you’ve made your purchase, it will show up in your Groupon purchase list after a few minutes (you should get an email to confirm that the Avios are ready).
Click the green button and you will be taken to a new page to get the Avios.

On the left side there should be a green button underneath a picture of an Iberia plane. Click the button and a pdf file will open in a new tab. At the top left there should be a security code and a coupon code. You will need these codes so make a note of them (ignore the ‘ref’ code).

Towards the bottom of the previous page, there’s a set of instructions. In the first paragraph there should be a small link. Click it, and you’ll be taken to a new page with some fields to fill in.

Add the security code, the coupon code, your email address, click the tick box, and hit the ‘validate coupon’ button. It may not work first time, and will just reload the page - this always happens for me. It will eventually work, just be patient. On the second attempt, it worked and took me to a new page asking for my Iberia Plus number. Enter it, hit the button, and you should get a confirmation message on the next page - your avios will be uploaded in 15 days.