The Torah is read with cantillation signs, that is, in a melody which suits the meaning of the words being read. Since the cantillation signs are not written in the Torah scroll, the reader must learn the signs that accompany the reading by heart. If there is no one present who learned the particular portion with cantillation signs, another person may look into a printed Chumash with the signs and whisper them to the reader, so that he can read from the Torah with the proper melody (Mishnah Berurah 142:8). If no one is able to read the Torah with cantillation signs, it is permissible b’dieved to fulfill the obligation of Torah reading without them (Shulchan Aruch 142:2).
It is necessary to be meticulous in the reading of the Torah. If the reader errs in reading a word, such that the meaning of that word is changed, he must repeat it properly. However, for a mistake which does not alter the meaning of the words, there is no need to repeat the reading.
Initially, it was customary that each person called up to the Torah would personally read his portion. For that purpose, everyone would prepare the whole weekly portion of the Torah reading. Alternatively, the gabbai would plan in advance the order of the people to be called up and notify each of them, so they could prepare their portions ahead of time. Yemenite Jews still do this nowadays.
However, from the time of the Rishonim, the majority of congregations became accustomed to appoint a Torah reader (ba’al koreh) who would read the Torah for everyone. The one called up recites a blessing on the reading before and after it, and the ba’al koreh reads the Torah for him. This way, people who do not know how to read the Torah are not embarrassed (Ran). This also avoids the possibility that people who erroneously think that they know how to read properly will be insulted if the gabbai does not call them up (Rosh). (See Shulchan Aruch 139:1-2; Peninei Halachah Likutim I, 4:6.)
. A Torah reader who left out a word, even if the meaning was not changed, must repeat the word. In a case in which he omitted a letter from a word without changing the meaning of the word, such as saying Haron instead of Aharon, according to the Mishnah Berurah 142:4 he need not repeat it, yet according to the Kaf HaChaim 142:2, he must.
If he erred in his reading of a word and continued on a bit, he must go back to the beginning of the verse in order to correct the mistake in such a way that the text will be understood correctly, and from there he continues reading in order. If the mistake is made in the first aliyah, and it is only realized during the third aliyah, the Mishnah Berurah rules (Bei’ur Halachah 142, s.v. “Machzirim”) that the congregation must return to the beginning of the verse in which the mistake was made and then continue reading in order from there until the end of the third aliyah. If, after they conclude the Torah reading, they realize the mistake, they return to the verse in which the mistake was made and read it along with another three verses. They do not recite a blessing on this second reading, because some maintain that b’dieved they fulfilled their obligation the first time even in reading with mistakes. See Peninei Halachah Likutim I, 4:13-14.