Firstly, follow the base game drinking rules, found here:

Additional rules:

• Whenever a Dragon Strength Token is placed in the Dragon Strength Box, everyone except the House Targaryen player takes a shot
• Whenever a Dragon unit dies, the House Targaryen player takes a shot
• Whenever the House Targaryen player uses their power tokens to support another player in bidding, the supported player and the House Targaryen player divide amongst themselves a number of sips equal to the number of power tokens the House Targaryen player contributed with.
• Whenever you purchase a loan from the Iron Bank, give away one shot plus a number of sips equal to the amount of power tokens paid, distributed among the other players as you see fit.
• Whenever one of your Vassal’s units dies, take 1 sip, regardless of the unit’s strength

Why it’s a good drinking game:

In addition to the qualities of playing the base game with drinking rules, the Mother of Dragons expansion gives you even more time to enjoy your beverage of choice, while also taking advantage of the asymmetrical nature of the House Targaryen gameplay, reflecting this in the new rules introduced.