Once you finish Act 3, each land you capture will begin to produce one unique ingredient. Check your kingdom map from time to time to harvest the crops.
Next, you need to learn potion recipes. You will get a couple of free recipes to begin with, and you can always find more of them in the [Shop]. Learning a new recipe is permanent: once you've read it, you know how to prepare this kind of potion for good.
Now that you have learned the recipes and got enough ingredients, go to [Craft] -> [Alchemy] to start cooking. Preparing a potion takes time, but you can fight, craft or plan your further upgrades while waiting. Or speed the process up with gems.