Alvin Plantinga begins his argument through presenting his concept of "possible worlds". A possible world is a certain way in which things can be. Therefore, there are an infinite number of possible worlds - one for every possible difference (no matter how seemingly insignificant) that there could be between them. Plantinga developed his argument in response to Malcolm, as he believed Malcolm's argument - although demonstrating the possibility for God's existence in some possible worlds - did not demonstrate the necessity of his existence in all possible worlds.
Plantinga defines God as "A being of maximal greatness". As a being of maximal greatness, it must therefore exist necessarily rather than contingently as if it depended on other factors for its existence it would not be maximally great. Plantinga uses the same logic as Malcolm for the next part of his argument; the existence of this maximally great being in a possible world must be either necessary or impossible. Since the existence of a maximally great being is not self-contradictory, its existence is not impossible. Therefore, a being of maximal greatness must exist necessarily in the possible world in question. In order for it to be necessarily true that this being exists, it must exist in all possible worlds. Therefore, a being of maximal greatness (God) exists necessarily in all possible world, including the actual world.
Bish, bash bosh! Nicely done, clear and succinct. You could use this as a supplementary version of the Ontological Argument, or as a point of comparison. If, however, you wished to use it as full 30-mark explanation of the Ontological Argument, you would not have enough detail and would need to do a bit more research into the context of Plantinga's work.
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