Even though A Christmas Carol is entertaining, how is it mainly intended to educate?
This is a great question. As you say, it is an entertaining story, to be sure, but there is an educational aspect as well. In fact, it is possible to argue that the educational aspect is the key component. Let me give a few points.
First, when Marley come to Scrooge in chains, as a ghost, this is intended to teach a lesson on greed. More specifically it is intended to teach the audience that money is not the answer. In fact, money can be the very thing that weigh us down in life. And in the end we all die and cannot take our wealth with us.
Second, the family life of Bob Cratchit is just the opposite. In their poverty, there is great joy, thankfulness and love. This point is meant to teach us that material things do not equal happiness. Happiness is found in family and people caring for one another.