The process of studying and learning as much as he can from one of the elementals was the first tentative steps in communication. He needs to understand how the elemental thinks, its motivations, and it's desires. A huge misunderstanding in the beginning (all mages go through this thought) is that the elemental is just a simple creature. What the wizard learns, later on, is that they have their own societies, families, and desires/needs that all humans have. They are the same as us.
Once the mage gets a feel for the elemental, the next step is to retrieve his Oracle Deck and start the communication process. The elemental is not going to come to the wizard because of force. He is going to come because of curiosity or desire.
The first step is for the wizard to lay down all of the Oracle cards face down. At that point, he'll concentrate on the elemental he has studied. Some of the cards will start glowing and the mage will feel a slight tingling when touching those cards. He will then turn over the cards that are glowing (there are usually 3 or more cards).
If he has studied enough, one of the cards will be the creature. The other cards will contain information about how to entice the elemental to come and visit the mage. This cannot be faked. If the wizard tries to just pick random cards, the cards will be blank when they turn over.