Frederick Copleston, A History of Philosophy, Volume I: Greece and Rome (Westminster: Newman, 1959) 218.
[For Plato, m]an's summum bonum or happiness includes, of course, knowledge of God--obviously so if the Forms are the ideas of God; while, even if the Timaeus were taken literally and God were supposed to be apart from the Forms and to contemplate them, man's own contemplation of the Forms, which is an integral constituent of his happiness, would make him akin to God.
Plato believed that things on earth are an imperfect reflection of eternal forms, or ideas, in heaven. For instance, a horse on earth is an imperfect reflection of the eternal horse form in heaven, the horse form being the idea of the perfect horse. And, against the Sophists, Plato maintained that there is an objective standard of justice. Societies may (and often do) follow it imperfectly, but the eternal form of justice still exists as a standard.
In Plato's dialogues, Socrates tries to bring people to a knowledge of the forms. Through a method of asking them questions and finding holes in their bad answers, Socrates hopes to guide them to a clear definition of justice, or virtue, or courage. For Plato, knowledge of the forms came through rigorous philosophy.
Plato maintained that a creator Demiurge fashioned the cosmos according to the forms. He also thought that human beings had some knowledge of the unseen forms, since they possessed some standard of beauty. As far as Plato was concerned, we wouldn't have a standard for the beauty of objects had we not encountered the perfect, beautiful forms that those objects imperfectly reflect. And that is Plato's proof for the immortality of the soul: our souls encountered the forms before entering our bodies, and so, in some manner, we remember them in our sojourn here. Yet, our knowledge of the forms is imperfect, and that is why we need rigorous philosophy to understand them.
God finding happiness by meditating on the forms makes sense to me, and yet it does not entirely. When God reflects on the forms, he is thinking about perfect justice, virtue, courage, etc., as well as the orderliness of nature, which is modeled on the forms. At the same time, nature has a lot of disorder, brutality, etc. Many Christians would attribute that to the Fall, while theistic evolutionists may assert that the brutality is a necessary part of nature's balance. My point is that nature can inspire us, but it doesn't always.
I like this passage from Copleston because it helps me to appreciate the God of the Greek philosophers. A philosophy professor once told me that Aristotle believed we should be like God, who's main activity was thinking about himself. I had a hard time liking a God who stared at his navel all day (speaking anthropomorphically). But, right now, I appreciate a God who gets pleasure out of contemplating order and beauty, as Paul exhorts believers to do in Philippians 4:8: "Finally, beloved, whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is pleasing, whatever is commendable, if there is any excellence and if there is anything worthy of praise, think about these things" (NRSV).