There was a bu yesterday with internet explorer preventing the adoption.
It was resolved yesterday.
To adopt just go to the adoption page, you can adopt all species. Just give a name (if you want), a gender and a birth place (if you want) and click adopt, you will then see the 6 eggs you adopted and their respective rarity.
The eggs are automatically added to your collection (in "my creatures")
If you have issues, feel free to contact me !