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What to add that has not already been said about what is perhaps the most famous of "speeches"? I think not much, so I will briefly summarize the object and the reason for the book.
First, the preface clarifies that it is a question of the work's approach not as an exposition of philosophy but as a preparation for it. Indeed, Descartes sees himself constrained by learning of the condemnation of Galileo for his ideas too accurate for the time to make consequent cuts on what should be the work at the base. His physics had been based on recent discoveries of Galileo - heliocentrism and the movement of the earth - he could not afford to corroborate these theses and risk condemnation himself. He, therefore, manages to be content to plow the ground without really planting anything, his seeds being dependent on ideas that he has no right to support.
He will explain his philosophical method to us, which he says should allow anyone who uses it to increase their knowledge by degree gradually. So this method, briefly, what is it?
We can say that he makes philosophy a science, not in so far as he creates concepts with the help of scientific formulas, but in the sense that he seeks truth, from which will flow truths, his method. So is scientific, but he applies it to philosophy. He doesn't want "maybe" and is fed up with contingency-based philosophies; he sees Stoicism as a magnificent palace built of sand and mud. This first truth will be the cogito.
Cogito ergo sums, I think therefore I am, the action of doubting necessitates that I believe, but if I believe, I must be, that I will be a thinking substance. This fact is the first brick of the vast building that Descartes erected.
Given European events, Descartes is satisfied with the minimum; however, this is not bad since it allows him to prepare for the assimilation of his philosophy. If his thought were work, the Discourse on Method would undoubtedly be its introduction.
Therefore, a fascinating work since it is the philosophical basis of a thinker who will have profoundly influenced all European and world thought; the cogito is universal with which all have confronted in one way or another. An accessible book, although it's the 17th century, imposes an old-fashioned style on us, convoluted turns of phrase, although sometimes very pretty.
It is to be read as one of the bases of modern philosophy but insufficient for anyone who wants to claim adequate knowledge of Cartesian thought.