Berachos Chapter 2, Mishnah 3. Our Mishnah deals with the proper way to recite Shema and with the status of someone who did not recite it properly.
"Hakorei es Shema velo hishmia le'ozno":
The Mishnah opens with the case of someone who recited Shema in a way that his ears did not hear his words. According to the first Tanna, "yatza" - he has fulfilled the mitzvah of reciting Shema. Rabbi Yosei disagrees and holds "lo yatza". The root of their dispute lies in how they expound the word "Shema":
According to Rabbi Yosei: "Shema" means that your ears should hear what your mouth utters, and therefore one who did not let his ear hear has not fulfilled the mitzvah.
According to the first Tanna: "Shema" comes to teach that in any language a person hears and understands, he may recite Shema. Although our practice is to say it in Hebrew, one can fulfill the mitzvah in any language he understands.
It should be stressed that even according to the first Tanna, this applies only after the fact, with regard to the act that was already done; but ideally one certainly must let his ear hear the words that come out of his mouth.
"Kara velo dikdek be'osiyoseha":
The Mishnah continues with the case of someone who recited but was not precise in the way he pronounced the letters: for example, a word that ends with the letter lamed followed by a word that begins with a lamed, so that when they are said together they are not distinct from one another and it sounds like a single word, and therefore they must be separated. The same applies wherever two beis's come next to each other. And if he did not separate them:
Rabbi Yosei says: "yatza" - he has fulfilled his obligation of reciting Shema.
Rabbi Yehudah says: "lo yatza" - he has not fulfilled the mitzvah.
The halachah follows Rabbi Yosei.
Even Rabbi Yosei agrees that ideally a person should be precise with the letters and careful in the way he recites. And this is worth reflecting on: people invest tremendous effort in order to hear the sound of the shofar properly, and go to great lengths to obtain a beautiful esrog. There are many positive commandments in the Torah, and we invest real effort to make sure that we are fulfilling them properly. Reciting Shema is also a positive commandment, except that the opportunity to fulfill it comes our way twice every single day. Every day and every recitation is an opportunity in its own right, and therefore it deserves the same measure of attention and thought that we give to the rest of the mitzvos of the Torah.
"Hakorei lemafrei'a - lo yatza":
The Mishnah teaches another interesting halachah: one who recites Shema out of order has not fulfilled the mitzvah. Reciting out of order means that he recites the last verse first, then the verse before it, verse by verse backwards. This is derived from the verse "Vehayu hadevarim ha'eileh" - "vehayu" means they shall be as they are, that the words should be in the form and the order in which they were presented, and one may not say them in reverse.
However, regarding the order of the paragraphs themselves, even though they have a fixed order, a person fulfills the mitzvah even if he said them in a different order: if he said "Vehayah im shamo'a" before "Shema", or "Vayomer" before all of them, he has fulfilled his obligation.
"Kara veta'ah - yachzor limkom sheta'ah":
The Mishnah concludes with this halachah: one who recited and made a mistake, such as skipping a letter, a word or a verse, returns to the place where he erred, to the beginning of the verse in which he made the mistake.
The Gemara on this Mishnah spells out the laws of doubtful cases:
He erred between one paragraph and the next: he knows that he finished a paragraph, but he is not sure where he is holding - he returns to the first paragraph, meaning to the first break between them, which is the beginning of "Vehayah im shamo'a"; this is how Rashi explains it. The Rambam explains that he must return to the beginning of the break.
He knows that he is in the middle of a paragraph but is not sure where: he returns to the beginning of that paragraph which he knows he is in.
He reached "uchsavtam": the phrase "uchsavtam al mezuzos beisecha" appears both in the first paragraph of Shema and in the second paragraph. If he does not know which of the two he is in, he returns to the first paragraph and completes it, and afterwards says "Vehayah im shamo'a".
He reached "lema'an yirbu yemeichem": this is the verse that follows "uchsavtam", and in this case he assumes that he was in the second paragraph and completes it, since out of habit he continued and reached "lema'an yirbu yemeichem", and he surely said the second paragraph as well.
In summary: in this Mishnah we learned the laws of reciting Shema properly: the dispute between the first Tanna and Rabbi Yosei regarding one who did not let his ear hear, rooted in how they expound the word "Shema"; the case of one who was not precise with the letters, where the halachah follows Rabbi Yosei that he has fulfilled his obligation, even though ideally one must be precise; the law that one who recites out of order has not fulfilled his obligation, derived from "Vehayu hadevarim ha'eileh" - they shall be as they are, as opposed to changing the order of the paragraphs, which does not invalidate the recitation; and finally the case of one who recited and made a mistake, that he returns to the place where he erred, along with the details of the doubtful cases that the Gemara explains.