I had one of the NPCs, Rhobart, teach me the Alchemy skill and explain me the recipe. But then, when I try to activate the Alchemy table, my character won't do anything.
Well there is no possibility to brew Beer in Risen!
When you first get the alchemy skill, you will get the recipe for the small heal potion. Right-Click on the Recipe in your inventory, then you will be able to create those potions at the alchemy table.