What exactly is Plato's position concerning the existence of God? Also,In which of his works can I find references to God? Is the position of Aristotle somewhat similar in the existence of God? If not, how does he differ? Any help with this would be appreciated.
The first problem with your question is that you talk of "God" with a capital G. This doesn't exist in Plato, and, for that matter in ancient greek litterature, because God is not the name of a person but a common noun. Thus Plato speaks of "the gods (hoi theoi), or "the god (ho theos)", in some cases of "god", but then in the same way we would talk of "man", using the word as a generic name. He also speaks of "the divine (to theion)".
Thus, if by "God" you mean the god of christianity, Yawhe, the Holy Trinity and the like, there is none of it in Plato or Aristotle. However, if you are looking for "traces" in Plato and Aristotle of a concept that somehow anticipates this god, or if you want to know what is their stand as regards what we are used to call "religion", this is another matter.
Then you want to know what concept of "god" you are looking for. Is it the concept of a single "god", that is, of a monotheistic religion? Is it the concept of "god the maker of heaven and earth, of all that is seen and unseen"? Is it the concept of the "Logos that was in the beginning, the Logos that was in God, the Logos that was God"? Or is it yet something else?
If you are looking for Plato's "religion", I think you should mostly look at book X of the Laws, and at the Timæus (as a whole, I would add). But this is only part of the answer. I think Plato knew perfectly well that on such matters, it is impossible to give complete answers with human words. Thus, he tried to approach the question from different angles and give partial complementary (and not contradictory) answers, both negative (what gods are not, what we should not believe) and positive (what we may safely believe about gods and the divine, and questions of "origins" and "ends").
In that respect, the answers he gives in the Timæus have to be "qualified" by the purpose of this dialogue: it purports to show man how he should look at the kosmos, that is "theorize" it (from theorein, which means in Greek "contemplate"), to find in it traces of an organizing "intelligence" and use it as a model for our organizing work as builders of lawfull cities as "just" men endowed with logos that is, a divine parcel in our own souls. And you must keep in mind that Plato himself repeats times and again that he does not states definite truths but tells only "likely myths".
In it, you will find not "God", but a "demiourgos", that is a "worker" (etymologically, demiourgos means "one who works for the demos, that is for the people"), which is immortal by nature but works from a model and has to deal with anagkè, necessity. Though he does not seem to be the maker of "place (chôra)" and matter, he is the maker of time, "a moving image of eternity", and of "lower" gods, that are only immortal by his will. These gods represent the immortal living creatures that are needed to have all sorts of creatures in the kosmos. They are the makers of man as the "host" of a divine soul (the logos) handed them by the demiourgos. But you will also read that the kosmos is often refered to as a "god", endowed with a soul.
In the Laws, you will find what Plato deems the needed "religion" to ensure order in the city. Basically, men have to hold three key tenets: that gods exist (that is, that the world is not a purely "material" thing, product of chance or necessity); that they care for the world; and that they cannot be "bought" or corrupted by men's gifts or prayers. But there, he makes clear that he does not pretend to give the last answer on such difficult questions.
In it you will find also the root of Aristotle theory of the unmoved mover. But whereas Plato is well aware of the limits of his own discourse, Aristotle wants to give complete answers and thus takes "litteraly" what was for Plato only an partial insight into possible answers.
And then, there is the question of "forms" and especially of "the good that is beyond being" (Republic, VI). But this would lead us too far away. And the question of how litteraly Plato himself would take his own "myths". Eventually, if you want to know what Plato thinks about "the divine", you may have to read all the dialogues, and see how it fits within his suggested answers to such questions as the purpose of life, the role of reason in man, the relationship of becoming to being, of time to eternity, of visible to intelligible, and so on...
Another problem with your question has to do with the term "existence", which would require that we investigate the concept of "being" in Plato and Aristotle. The key to this problem, for Plato, lies in the Sophist: "being" is the least meaningfull predicate of all. To say that something "is", is to say nothing at all until you say "how" it exist, that is, to what other forms it "participates", and for what purpose it "is", that is, what its "good" is. As soon as you say "god", it "is"; that is, there is at least something in your mind that "is" in a certain way. But then , does it relates to some other "being" outside your mind, that is the question. Thus, the problem is not "existence" but "relations" (kind of an anticipation of some of Augustines' theories on the Trinity).
Source: http://plato-dialogues.org/email/960211_1.htm
The first problem with your question is that you talk of "God" with a capital G. This doesn't exist in Plato, and, for that matter in ancient greek litterature, because God is not the name of a person but a common noun. Thus Plato speaks of "the gods (hoi theoi), or "the god (ho theos)", in some cases of "god", but then in the same way we would talk of "man", using the word as a generic name. He also speaks of "the divine (to theion)".
Thus, if by "God" you mean the god of christianity, Yawhe, the Holy Trinity and the like, there is none of it in Plato or Aristotle. However, if you are looking for "traces" in Plato and Aristotle of a concept that somehow anticipates this god, or if you want to know what is their stand as regards what we are used to call "religion", this is another matter.
Then you want to know what concept of "god" you are looking for. Is it the concept of a single "god", that is, of a monotheistic religion? Is it the concept of "god the maker of heaven and earth, of all that is seen and unseen"? Is it the concept of the "Logos that was in the beginning, the Logos that was in God, the Logos that was God"? Or is it yet something else?
If you are looking for Plato's "religion", I think you should mostly look at book X of the Laws, and at the Timæus (as a whole, I would add). But this is only part of the answer. I think Plato knew perfectly well that on such matters, it is impossible to give complete answers with human words. Thus, he tried to approach the question from different angles and give partial complementary (and not contradictory) answers, both negative (what gods are not, what we should not believe) and positive (what we may safely believe about gods and the divine, and questions of "origins" and "ends").
In that respect, the answers he gives in the Timæus have to be "qualified" by the purpose of this dialogue: it purports to show man how he should look at the kosmos, that is "theorize" it (from theorein, which means in Greek "contemplate"), to find in it traces of an organizing "intelligence" and use it as a model for our organizing work as builders of lawfull cities as "just" men endowed with logos that is, a divine parcel in our own souls. And you must keep in mind that Plato himself repeats times and again that he does not states definite truths but tells only "likely myths".
In it, you will find not "God", but a "demiourgos", that is a "worker" (etymologically, demiourgos means "one who works for the demos, that is for the people"), which is immortal by nature but works from a model and has to deal with anagkè, necessity. Though he does not seem to be the maker of "place (chôra)" and matter, he is the maker of time, "a moving image of eternity", and of "lower" gods, that are only immortal by his will. These gods represent the immortal living creatures that are needed to have all sorts of creatures in the kosmos. They are the makers of man as the "host" of a divine soul (the logos) handed them by the demiourgos. But you will also read that the kosmos is often refered to as a "god", endowed with a soul.
In the Laws, you will find what Plato deems the needed "religion" to ensure order in the city. Basically, men have to hold three key tenets: that gods exist (that is, that the world is not a purely "material" thing, product of chance or necessity); that they care for the world; and that they cannot be "bought" or corrupted by men's gifts or prayers. But there, he makes clear that he does not pretend to give the last answer on such difficult questions.
In it you will find also the root of Aristotle theory of the unmoved mover. But whereas Plato is well aware of the limits of his own discourse, Aristotle wants to give complete answers and thus takes "litteraly" what was for Plato only an partial insight into possible answers.
And then, there is the question of "forms" and especially of "the good that is beyond being" (Republic, VI). But this would lead us too far away. And the question of how litteraly Plato himself would take his own "myths". Eventually, if you want to know what Plato thinks about "the divine", you may have to read all the dialogues, and see how it fits within his suggested answers to such questions as the purpose of life, the role of reason in man, the relationship of becoming to being, of time to eternity, of visible to intelligible, and so on...
Another problem with your question has to do with the term "existence", which would require that we investigate the concept of "being" in Plato and Aristotle. The key to this problem, for Plato, lies in the Sophist: "being" is the least meaningfull predicate of all. To say that something "is", is to say nothing at all until you say "how" it exist, that is, to what other forms it "participates", and for what purpose it "is", that is, what its "good" is. As soon as you say "god", it "is"; that is, there is at least something in your mind that "is" in a certain way. But then , does it relates to some other "being" outside your mind, that is the question. Thus, the problem is not "existence" but "relations" (kind of an anticipation of some of Augustines' theories on the Trinity).
Source: http://plato-dialogues.org/email/960211_1.htm