To earn a Divine Dragon, you first need to acquire the item "Sigils" for the current season. They can be obtained from claiming event rewards and opening bronze, gold or super sigil chest. Please note that they do not roll over to the next season as each season requires a different set of Sigils.
Once you have enough sigils, you will be able to choose from different Divine Dragons available for the Season. Please note that once the season ends, you can no longer get the dragon or their evolution stone forever.