Before you can enter into a cultural goods treaty you have to research Cultural Exchange (Science) and must have at least one museum. Now you can enter into a cultural goods treaty with any other player as long as their also have a museum. For each treaty you receive one cultural good that you can exhibit in your museum. Every exhibit increases the satisfaction level of the citizens in your town.
Tip: You can only enter into as many cultural goods treaties as the museum expansion stage. Multiple museums on different colonies will be added. Furthermore you can only exhibit as many cultural goods in your museum as the number of expansion stages for that museum.
in order to get +1 cultural good, you have to send a treaty: click diplomacy on person you wish, then drop down menu 'cultural goods'... if the other player accepts you both gain +1 cultural good.