The God of the Reformed church is an all-powerful God. Calvin in particular stressed this point at every turn. For example, in the Institutes of the Christian Religion Calvin discussed miracles, and took as an example the wind God stirred up in the story of Jonah that caused the sailors to draw straws and throw Jonah overboard. The point to take away from this story, according to Calvin, was not that God is powerful enough to intervene in nature and cause miraculous occurrences. The point to take away was that no breeze, no matter how commonplace, ever arises without the conscious active decision of God to make it blow. Calvin believed that every single occurrence, the most mundane as well as the most spectacular, was equally miraculous, a direct act of God.
Calvin's most common image for God is loving father. This is a very important point, because the common characterization of Calvin is a misinterpretation (though it may be an accurate interpretation of some Calvinists, for example in the Dutch Reformed Church represented in the Synod of Dort). For Calvin, the very definition of faith is to trust that God has our best interests at heart, even when things do not seem to be going our way; this is a common experience that children have of their human fathers.
Most people who learn of Calvinism learn first of predestination, the doctrine that God chose at creation who would be saved and who damned. This seems cruel and arbitrary. But for Calvin there is no other way to think of God if we want to take sovereignty seriously. And it is crucial to note where in his theological system Calvin chooses to explain this doctrine. It does not come in Book I of the Institutes of the Christian Religion, where Calvin discusses the nature of God. Rather, it comes in Book III where Calvin discusses the benefits of faith. In other words, it ought not to be the first thing one thinks of about God. It certainly ought not to be the object of curious speculation. But for those who have been saved it comes as added relief to know the extent of control held by the God who saved them.
Calvin agrees with Luther that fallen humans cannot draw analogies from nature or their own reason and morality to the nature of God. Here we see the influence of the medieval nominalists. All we know about God is what God has chosen to reveal to us in scripture. God reveals this to us not to satisfy our curiosity (why is the universe not set up differently?) but to save us. And Calvin thinks a plain reading of scripture indicates predestination. It was not a doctrine he chose (he calls it a "horrible decree"), but one revealed to us in a history of God's choices-Abel over Cain (Genesis 4), Jacob over Esau (Genesis 25-27), Joseph over his brothers (Genesis 37), David over Saul (1 Samuel 16).
Reformed Christians maintain the traditional Christian doctrine that God is a Trinity, three persons in one God (Father, Son, and Holy Spirit). God the Father is the creator; the Son is God incarnate (born in the flesh) who, by his sacrifice on the cross saves humans from sin; the Spirit is the active presence of God in the Church and in history. Calvin made the interesting argument in the Institutes of the Christian Religion that scripture's presentation of God as a Trinity is a way of combating human idolatry: polytheists (those with more than one God) clearly do not worship the true God, but neither do those without the doctrine of the Trinity. Jews and Muslims, for example, who are monotheists (believe in one God), are in danger of believing that they have captured the essence of God with this belief-the Trinity ensures that we worship just one God, but that we never make the mistake of forgetting that the nature of God is fundamentally a mystery to humans.
Calvin maintained the traditional Christian doctrine of the two natures of Christ (fully human and fully divine) defined at the Council of Chalcedon in 451. While it is difficult to conceive of a being both fully human and divine, Calvin believed this was the clear teaching of scripture (especially John 1:14). It was also necessary for Calvin's traditional theory of substitutionary atonement-humans owed God an infinite debt for sin. Only a human could pay the human-incurred debt, but because it was infinite it could only be fully dealt with by God. Thus a God-man is in some sense necessary.
For Calvin, as for Luther, the devil is not a metaphorical being but an actual being whose task it is to confuse humans and tempt them into damnation. For example, in the controversy of the Lord's Supper, which was the main theological issue that kept the Lutherans and Reformed from uniting into one Protestant church, Calvin saw the hand of the devil stirring up dissension. Similarly, angels are beings sent by God to do God's work, to protect humans, and to counteract the activities of the devil.