Aristotle was born in Stagira, Greece, in 384 BC. He was sent to be a student at Plato's Academy, and eventually became a teacher there himself. He was the tutor of Alexander the Great. When Plato died, and Aristotle was not chosen to take over Plato's Academy, he formed his own school in Athens called the Lyceum. Aristotle wrote about almost everything, including medicine, physics, astronomy, biology, law, logic, and government, to name a few. Many of his writings form the basis of Western thought.
He knows that we see the moon by the light of the sun, how the phases of the moon occur and understands how eclipses work. (The Greeks had known this for a while.)
Aristotle knew that the earth was a sphere. Philosophically, he argues that each part of the earth is trying to be pulled to the center of the earth, and so the earth would naturally take on a spherical shape. (Gravitationally, this is actually accurate!) He then points out observations that support the sphericalness of the earth. First, the shadow of the earth on the moon during a lunar eclipse was always circular. The only shape that always casts a circular shadow is a sphere. Second, as one traveled more north or south, the positions of the stars in the sky change. There are constellations visible in the north that one cannot see in the south and vice versa. (He uses this to also argue that the earth isn't very big, because you don't have to travel very far to notice the difference.) Third, he says not to discount those who say that Morroco and India are really close to each other, because there are elephants in both of these regions. (De Caelo, Book II Part 14)
Aristotle talks about the work of Eudoxus and Callippus, who had developed an earth centered model of the planets. In these models, the center of the earth is the center of all the other motions. While it is not sure if Eudoxus and Callippus actually thought the planets moved in circles, Aristotle certainly does. Aristotle even adds "counteracting spheres" so that the motion of one sphere doesn't interfere with the motion of the one next to it. To Aristotle, the many spheres that carry the planets, including the sun and moon, are very real, and he says there are 55 of them. (Metaphysics, Book XII, Part 8)
Aristotle rejects a moving earth for two reasons. Most important is that he doesn't understand inertia. To Aristotle, the natural state for an object is to be at rest. He believes that it takes a force in order for an object to move. Using Aristotle's ideas, if the earth were moving through space, if you tripped, you would not be in contact with the earth, and so would get left behind in space. Since this obviously does not happen, the earth must not move. This misunderstanding of inertia confuses people until the time of Galileo. A second, but not as important, reason Aristotle rejects a moving earth is that he recognized that if the earth moved and rotated around the sun, then "there would have to be passings and turnings of the fixed stars": the positions of the stars would change with the seasons. (De Caelo, Book II, part 14) In modern words, there would be an observable parallax of the stars. One cannot see stellar parallax with the naked-eye, so Aristotle concludes that the earth must be at rest. (The stars are so far away, that one needs a good telescope to measure stellar parallax, first measured in 1838.)
Aristotle believes that the objects in the heavens are perfect and unchanging. Since he believes that the only eternal motion is circular with a constant speed, the motions of the planets must be circular. This comes to be called "The Principle of Uniform Circular Motion" and even Copernicus believes in it. The perfectness and constancy of the heavens ends up being challenged in the late 16th century when Tycho Brahe shows that a supernova and a comet are beyond the orbit of the moon.
Aristotle and his ideas become very important because they become incorporated into the Catholic Church's theology in the twelfth century by Thomas Aquinas. In the early 16th century, the Church bans new interpretations of scripture in a defensive move against the growing Protestant movement. At the time, there had been no interpretations involving a moving earth; thus teaching a non-geocentric model of the solar system becomes a bad thing to do.