Reason distinguishes men from animals. Members of the same species share certain essential qualities, so every man has "common sense." (When opinions differ, it's due to a difference in available evidence.)
Collaborative efforts to find truth are rarely as successful as the efforts of one man. Laws invented democratically aren't as good as laws developed by a single legislator, and laws laid down by God are "incomparably superior."
Descartes decided to build the first indisputable philosophical foundation. It will consist entirely of his own ideas, rather than a mere reformation of ideas previously given to him. Not everyone should use this philosophical method because they may have difficulty judging what is true or abandon their beliefs without rebuilding them.
His philosophical method, based on mathematical proofs, has four parts: Delay judgment until certain; Divide the problem into parts; Start simple and become more complex; Enumerate and review fully to prevent omissions. He will question everything he thinks he knows, and consider false anything that is "merely plausible," to distinguish "sand" from "rock" and secure the foundation. While rebuilding his beliefs, he needed a "provisional code of morality," which also has four parts: Obey the country's customs; Act decisively without second-guessing; Change oneself rather than dwelling on what cannot be changed in the world; Choose the best profession.
The entire world may be nothing more than a dream, but Descartes knows he exists because he is the one thinking. I think, therefore I am is the first principle of his new foundation. Because he can imagine himself without a body, his thinking soul is distinct from his body. We can know things without using the five senses--in fact, ideas which we "conceive clearly and distinctly" through reason are always true, given by God. All concepts are in some way founded in truth, or God wouldn't have given them to us. Belief in God reassures that all perceptions aren't merely a dream.
The idea of God entails his existence just as the idea of a triangle entails that its angles equal 180 degrees.
Less perfect beings depend on God and cannot exist without him. The less perfect can't generate the idea of the more perfect. Because Descartes can think of something more perfect than himself (i.e., God), he concludes God exists and put the idea in his head.
God can't have imperfections like "doubt, inconstancy, sorrow" or dependency. God isn't a body-mind composite because otherwise his parts would depend on each other.
Even handicapped humans talk or gesture to communicate thoughts, while animals don't. Animals are therefore essentially different from humans, lacking capacity for rational thought. Cardiac circulation of heat and "animal spirits" makes it possible for bodies to move without conscious intent. Humans bodies could have existed like animals, but God endowed us with souls.
The soul is not apparently vulnerable to any particular thing, so it's immortal. Lack of belief in immortality is the thing most likely to make one stray from virtue.
Rene Descartes. Discourse on the Method of Rightly Conducting the Reason and Seeking Truth in the Field of Science. (1637) Published in Discourse on Method and Meditations. Translated by Laurence J. Lafleur. Indianapolis: Bobbs-Merrill Educational Publishing, 1960.
This summary was written in 2005, along with a series of other 500-word summaries of philosophy books, as an exercise in brevity.