How do you unlock rank 2 and 3 alchemy recipes in World of Warcraft: Battle for Azeroth?

• Rank 1 recipes are not special and simply allow you to craft the item. You can learn Rank 1 recipes from your profession trainer.
• Rank 2 recipes lower the amount of reagents needed for crafting. Most Rank 2 recipes can be purchased from the Alchemy trainer once you reach a high enough skill level, however some such as Mystical Cauldron are acquired differently.
• Rank 3 recipes have a chance to create multiple extra items at no extra cost. They are harder to obtain, often coming from faction vendors that require a certain reputation level before you can learn it.

Source

Hold your mouse over the stars of the rank in the recipe's window and the tooltip tells you where to obtain the next rank and what the ranks do. This way you don't have to search for every single recipe.