In Greek mythology, Apollo and Dionysus are nearly opposites of one another, and as with many opposites, life would not operate just quite right without both of them. They each played a specific role for the Greeks. They had very different things associated with them.
Apollo was often associated with logic and the power of the mind. He was basically in charge of the Work section of the people. Logic is something the Greeks used often, and when they didn't, things often happened for the worst. He is also associated with intellect. The followers of Apollo would consist of those who strongly believed in the things he was thought to control. These people would believe in logic, they would believe in reason, and they would also pay attention to the power of the human mind. Another thing Apollo is associated with is music, so he would also be worshipped by music lovers.
Apollo is worshipped in religion to provide his followers with logical thought and a good intellect. As for Greek thought, he was also very in control of this. The Oracle at Delphi, mentioned in, but not only in, Sophocles' Oedipus Rex. The Oracle was there to bestow knowledge from Apollo onto those who came to it. Another reason people looked to Apollo was to help heal the sick and the dying, because he is associated with medicine, probably because of his vast knowledge.
Dionysus, on the other hand, represents the Play side of life. He is the god of emotions, the god of wine, and also the god of fertility. Some things attributed to Dionysus are the dithyrambs, or choral hymns, sung for him but the people. This was how they praised him. Drama is also directly associated with him. Being the god of wine and the god of fertility led to some very strange things in situations where Dionysus prevailed over Apollo. Many drunken orgies took place during this time.
The Dionysion followers might be thought of as all the people who enjoyed wine, the people who...