1. It is possible that God exists
2. If it is possible that God exists, then He exists in some possible world
3. If God exists in some possible world, then He exists in every possible world
4. If God exists in every possible world, then He exists in the actual world
5. If God exists in the actual world, then God exists
6. Therefore, God exists
The only premise that is really of controversy is premise one (Craig 93-157). Is it logically possible that God exists? Well the only reason we would have for doubting that it is logically possible is if God was an incoherent being such as a married-bachelor
This argument has not gone without some objections however. One of the objections is that you can recast the argument to show that a unicorn exists in the actual world (Kenneth, “Anselm’s Ontological Argument for the existence of God”, pp. 1-12). However, this objection is seriously confused when it comes to modal logic. Modal logic deals with possibilities, impossibilities, and necessities. A unicorn by definition is a contingent being who only exists in some possible worlds. If a being only exists in some possible world, then it does not follow that it exists in every possible worlds and thus the actual world. God, however, is defined as a metaphysically necessary being. So if it is possible that God exists, then He would have to exist in our actual world!
Another objection to the argument is that it is a trick. But what you will find is that the types of people with this objection do not have much experience in the realm of philosophy. The nature of the modal ontological argument is that if the premises are true, then the conclusion necessarily follows. In other words, given the nature of deductive arguments one has to deny one of the premises if they are going to disagree with the conclusion. It does not matter if you do not like the conclusion, nor does it matter if you disagree with the conclusion.