Explain Anselm's Ontological Argument

It is widely believed that Anselm wrote this argument as a prayer to God; Anselm wrote from the position of someone with ‘faith seeking understanding’, not of someone trying to logically prove God's existence. Anselm's argument uses deductive logic, an a priori logical position and uses reduction ad absurdum reasoning. It is formed in two parts:
Premise 1: God is something “than which nothing greater can be thought” of – if you can think of a greater being, then that being is GodPremise 2: Things exist either in mind only (in intellectu) or in mind and reality (in re)Premise 3: It is better to exist in mind and reality than in mind onlyConclusion: Therefore God must exist
However Gaunilo wrote a reply claiming that Anselm’s logic is absurd since it could be applied to anything. He says we have an understanding of many things but that does not make them exist. He uses the example of a lost island which is the greatest conceivable island. By Anselm’s logic that island must exist too. Anselm replied:
Premise 1: God is something “than which nothing greater can be thought” ofPremise 2: Things exist either contingently or necessarilyPremise 3: It is greater to exist necessarily than contingentlyConclusion: Therefore God must exist
These two arguments form Anselm's Ontological Argument