Copernicus was the youngest of four children. After his father's death when he was only 11 years old, Copernicus and his siblings were adopted by his uncle, who would later become Bishop of Ermland. Copernicus was able to go to school, and eventually to the University of Cracow, and then later on to Italy to continue his studies in law, mathematics, astronomy and medicine. He finally returns to Poland for good in 1506, and after his uncle dies in 1512, he becomes a canonist at Frauneburg. (This means that he works for the Catholic Church, but he is not a priest.) Copernicus is able to support himself and find enough time to continue to do astronomy. He works on astronomy for most of his life, but mostly alone and as a hobby.
Copernicus believed in the Principal of Uniform Circular Motion - possibly even more so than Ptolemy. He objects to the Ptolemy's invention of the equant as a violation of that principal. He ends up proposing a heliocentric theory, while still relying on circles and epicycles, does not use the equant. Around 1511, he circulates a little manuscript called Commentariolus in which he lays out a general framework for a model of the solar system, which he bases on the following seven postulates:
He doesn't offer any real details of the theory, just lays out what things would look like. He promises a fuller version in the future, and he works on his theory for the next 30 years.
There are some important points regarding these postulates. He has to say that the stars are really far away to account for the fact that there was no visible stellar parallax. (Remember that there were some real science reasons why the Greeks had originally rejected a moving earth - and one of them was the lack of an observable stellar parallax.) Also, the sun does not have any role in the mechanics of the solar system; it is simply hanging out near the various centers of the orbits of the planets. In fact, Copernicus does not concern himself with any causes of the motions, all he is trying to do is mathematically model them. It is hard to show how retrograde motion actually occurs, so I won't try and do it here. (A good outside link is http://faculty.fullerton.edu/cmcconnell/Planets.html) Retrograde motion happens when the earth is lapping an outer planet, or when an inner planet is lapping the earth. If it still doesn't make sense, see me in school, and I can show the stupid little "retrograde" program. (I should really make a java version, but then, I don't know java...) Additionally, there is a great shockwave file which I got from http://astro.unl.edu/naap/ssm/ssm.html. (To see the retrograde motion, look at the "Zodiac Strip" in the bottom left and watch how the planet moves along the zodiac, as seen from the earth.)
In 1543, the full treatment of the heliocentric theory, De Revolutionibus Orbium Coelestium, is finally published. It is very possible that the book might never have been published were it not for a young astronomer, Joachim Rheticus, who visited Copernicus in 1539 to find out for himself the details of a supposedly new heliocentric theory. Copernicus lets Rheticus write a small favorable report on the new cosmology, and after he leaves in 1541, gets Copernicus to agree to send the completed manuscript to him for printing. Rheticus then arranges for the book to be printed by one of the best technical printers around, but unfortunately Rheticus himself ends up getting a new job and cannot oversee the printing directly. The printer enlists the help of a local technical proofreader, Osiander, who ends up adding his own introductory paragraph to deflect the certain criticism of the moving earth hypothesis. He argues that the heliocentric theory is only a mathematical convenience, and not supposed to actually represent reality. Osiander ends by saying, "And as far as hypotheses go, let know one expect anything in the way of certainty from astronomy, since astronomy can offer us nothing certain, lest, if anyone take as true that which has been constructed for another use, he go away from this discipline a bigger fool than when he came to it." (Copernicus, p. 4.)
Copernicus probably only saw the first copies on his deathbed. The book itself is a masterpiece - and mirrors Ptolemy's work in scope and ordering. (Since he was working by himself in his spare time it is no wonder it took him 30 years to produce.) Ptolemy's work was so successful and so well-accepted, perhaps Copernicus knew that he needed to produce a model as detailed and all-inclusive as Ptolemy's. This is the first competitor to Ptolemy's theory in over 1400 years. As is done in the Almagest, he includes star charts and mathematical tables - everything one would need to start using the model and computing planetary positions.
It is important to stress what Copernicus' model was and wasn't, as there are many misconceptions regarding what he said. This is the first truly worked out heliocentric theory in history and Copernicus is making a bold leap saying the earth is just another planet and going around the sun. However, his model is not any more accurate than Ptolemy's. Mathematically, the two models are identical - they both are based on the idea of circles and constant speeds.
Some people love the Copernican model, some people hate it. People did not like the Copernican theory becuase it was more accurate than Ptolemy (it was the same) or because it was easier to use than Ptolemy (it was the same.) They really liked it because the Copernican model got rid of the equant and was truly a planetary system. In the Copernican system, the ratios of the planetary orbits are fixed; they depend on each other. Mars, for example, has an average distance to the sun that is 1.5 times that of the earths. In the Ptolemeic model, the orbital parameters for an individual planet were independent of all the other planets and had nothing to do with each other. If one wanted to make Mars the farthest planet from the earth, one easily do that. Not so in the Copernican system. To simplify this argument, the Copernican model was prettier than the Ptolemeic model. In the preface to De Revolutionibus, Copernicus says, "Moreover, they have not been agle to discover or to infer the chief point of all, i.e., the form of the world and the certain commensurability of its parts. But they are in exactly the same fix as someone taking from different places hands, feet, head, and the other limbs - shaped very beautifully but not with reference to one body and without correspondence to one another - so that such parts mde up a monster rather than a man." (Copernicus, p. 5.) For those who appreciated the beauty of the mathematical model, it was possible to adopt the logic of Osiander's preamble, and treat the heliocentric hypothesis as a useful methematical tool, but not necessarily implying that the earth actually does move.
So why did some people really dislike the Copernican model? In short, they could not get over the fact that we don't sense that the earth is in fact rotating on its axis and going around the sun. Science had still not figured out what inertia was, and people honestly thought that if the earth were rushing through space trying to go around the sun, then every time you jumped up in the air, you would get left behind by the fast moving earth. Because of this, a lot of people could not accept a planetary model that involved a moving earth. Writing about Copernicus' work, Tycho Brahe said, "This innovation expertly and completely circumvents all that is superfluous or discordant in the system of Ptolemy. On no point does it offend the principal of mathematics. Yet it ascribes to the earth, that hulking, lazy body, unfit for motion, a motion as quick as that of the aethereal torches..." (Gingerich, p. 181.)
In the beginning of De Revolutionibus, Copernicus defends the concept of a moving earth in a couple ways. He first makes an argument for a moving earth based on the speeds of the stars. He points out that the stars have to be moving incredibly fast if they do in fact circle the earth, even faster than the earth would be in orbit around the sun. Copernicus answers the "inertia issue" by simply comparing the earth to a boat that is traveling on the ocean when it is smooth sailing: "As a matter of fact, when a ship floats on over a tranquil sea, all the things outside seem to the voyagers to be moving in a movement which is the image of their own, and they think on the contrary that they themselves and all the things with them are at rest. So it can easily happen in the case of the movement of the Earth, that the whole world should be believed to be moving in a circle." (Copernicus, p. 17.)
The biblical basis for insisting on a stationary Earth came from a few scattered sentences in the Bible which talk about a moving sun, implying that the Earth was at rest. Both the Lutherans and Catholics largely followed the logic of Osiander's preamble, and treated the book as a mathematical exercise, and it was generally very well regarded. Many astronomers did not get caught up in whether the earth actually moved or not, they just liked the mathematical beauty of the Copernican system. Seventy years later, De Revolutionibus does get put on the list of prohibited books by the Catholic Church, but that is only after Galileo, and for that matter Kepler, becomes a very vocal proponent of the heliocentric theory, arguing that it is not merely a mathematical convenience, but physical reality. (Both Galileo and Kepler wrote about reconciling Biblical verses with a heliocentric universe, arguing that the Bible could still be infallible, yet the Earth still move.)
There are some additional "philosophical" reasons why some astronomers did not like the heliocentric model. Being simplistic, it introduces more than one center of motion, as the moon goes around the earth and the earth goes around the sun. (I say simplisitic because the centers of the epicycles are already all different.) The Ptolemeic model is sort of cleaner because everything goes around the earth. Where people didn't understand inertia, and so really objected to a moving earth on "common sense" they also didn't get how the moon could get carried around the sun by the earth.
There is also the misconception that people didn't like the earth going around the sun because it removed the earth from the "special" place of the center of the universe. Reality was actually the exact opposite. In the 16th century, people argued that the earth had to be in the lowest, dirtiest place, and so must be sort of at the bottom of the universe, hence the stars and planets all had to be up far away and going around the earth. Placing the earth in orbit around the sun was actually promoting the earth to the special place in the heavens; people were still clinging to the Aristotelian concept that the heavens were all perfect and unchanging.