Here's how I taught the Ontological Argument for God's Existence in my Philosophy of Religion classes. I may share this in my coming Apologetics class in Renewal School of Ministry.
Anselm's Ontological Argument for God.
First: state the argument like this.
1. I have an idea of a being a greater than which cannot be conceived.
2. Therefore, God exists.
1. I have an idea of a greatest possible being.
2. Therefore, God exists.
Second: explain what it is like to have an "idea" of something (explain essential and contingent attributes).
Every time you have an idea of something, that idea has essential attributes and contingent attributes. Essential attributes are what makes that thing what it is, and without which it would not be what it is.
Use the example of a triangle. Essential attributes of "triangle" include: "having three sides," and "angles equaling 80 degrees."
A contingent attribute is a non-essential attribute. E.g., the triangle in my mind is "pink." "Pinkness" is not an essential attribute of triangularity; i.e., a triangle does not have to be pink in order to qualify as a triangle.
Third: Anselm claims to be able to conceive of "greatest possible being."
I can think, in my mind, of a greatest possible being. That is, I can have an idea of "greatest possible being." Because whenever I have an idea of anything, that idea has essential attributes (otherwise I could not have the idea), my idea of "greatest possible being" includes essential attributes of: "omniscience" (knows everything that can be known); "omnipotence" (is able to do everything that can be done); and "all-loving" (assuming it is greater to love than to hate).
OK. But why must such a being actually exist? Because...
Fourth: explain that, for Anselm, it is greater to exist in reality than in the mind alone.
"Existence," for Anselm, is a great-making attribute or property.
Therefore a greatest possible being (AKA "God") actually exists. Because if "actual existence" is not an essential attribute of "greatest possible being," then I am not thinking of "greatest possible being."
Fifth: explain why, for Anselm, if someone says "There is no God" then they are a "fool."
Because in order to say "There is no God" one must have a concept or idea of "God." Thus, that being the case, even the fool must acknowledge that God exists.
Finally: explain how, then, the argument works.
Anselm thinks his argument works because one cannot conceive or think of God as not existing, any more than one can think of a triangle that does not have three sides.
For an excellent article on the Ontological Argument see Internet Encyclopedia of Philosophy.