The Posuk in Nechemia (ח:ה) states that Ezra opened the Sefer Torah for all the nation to see, וכפתחו עמדו כל העם, "and upon his opening it the whole nation `stood.'" Rashi (שם ד"ה וכפתחו) writes that the Posuk means that when Ezra began to read the Torah the whole nation became quiet. Similarly, the Metzudas David (שם ד"ה וכפתחו) writes that when Ezra either opened the Sefer Torah or started to read everyone stopped talking. The Metzudas Tzion quotes a Posuk from Iyov where the word עמדו is used to mean be quiet. The Gemara in Sotah (לט.) writes that once the Sefer Torah is opened it is prohibited to talk even items containing Torah matter based on the Posuk in Nechemia (שם), since עמידה means to be quiet. However, while most מפרשים do indeed translate the word עמדו as being quiet, the Ibn Ezra writes that the Posuk means that when Ezra opened the Sefer Torah everyone stood on their feet in honor of the Torah. Likewise, the Ralbag comments that everyone stood on their feet and they did not move around in order to hear the reading.
The Gemara in Megillah (כא.) writes that unlike the reading of the Megillah, which can be done either standing or sitting, the Torah must be read only while standing based on a Posuk in Devarim. Both the Tur (או"ח ס' קמ"א) and the Shulchan Aruch (שם סע' א) codify this as the Halacha. Whether or not the rest of the congregation also has to stand will be discussed. The Shulchan Aruch (ס' קמו סע' ד) writes that the whole congregation does not have to stand while the Torah is being read. However, the Ramo (שם בהגה), as well as the Mordechai (שבת תכ"ב), both note that there are those who are strict regarding this,and that the Maharam used to stand for Torah reading.
The Magen Avraham (שם ס"ק ו) writes that only the reader has to stand, but everyone else including those standing on the Bimah are allowed to sit because the Torah is resting in its place and not moving. The Be'er Heitev (שם ס"ק ב) also writes that the obligation to stand for a Sefer Torah is only when it is moving, but when it is resting on the Bimah it is permissible to sit. The Vilna Gaon (ביאור הגר"א שם) quotes the aforementioned Gemara in Sotah that says the word עמידה means being quiet, thus prohibiting talking, but it is only the reader and the translator who have to stand during the reading. The Machatzis HaShekel explains that one does not have to stand for a different reason. The Torah during its reading is lying on the Bimah. The rule is that if something is 4 טפחים (handbreadths) by 01 טפחים, it is considered to be in a different domain, and if the Torah is in a different domain, then one would not have to stand. He even writes (שם) that the people standing on the Bimah would not have to stand, because whatever the Torah is placed upon is probably also considered to be a separate domain from the Bimah area where they are. The Beis Yosef (או"ח ס' קמא ד"ה וצריך) quotes the aforementioned Gemara in Megillah, and he writes that it was only talking about the reader, but the rest of the congregation may sit; the Perisha (שם אות א) rules the same way.
The Taz (או"ח ס' קמו ס"ק א), however, writes that when the Gemara in Sotah (שם) said that עמידה, means being quiet, it did not mean that being quiet is its sole meaning. It meant that in addition to standing one also has to be quiet. Indeed, he claims that the Maharam's practice is correct, and it is what we should all do. The Taz also quotes a Teshuvah of Rav Ovadyah Seforno (סימן ד) which concurs. The Bach (או"ח ס' קמא ד"ה וצריך) writes that even though technically one does not have to stand, it is worthy and proper to stand during the reading. He explains that since every person hearing the reader should picture in his mind that he is receiving the Torah at Har Sinai, it is proper to stand because at Har Sinai all of Bnai Yisrael were standing around the mountain. He quotes the Posuk in Devarim (ה:ה) which indicates this. The Aruch HaShulchan writes that one does not have to stand, but it is proper and a Kibbud HaTorah if one does. He brings down the fact that we were all standing at Har Sinai, and the Gemara in Sotah which says that after Rabban Gamliel died, Kibbud HaTorah left, also noting that during his time people used to stand while learning. The Pri Chodosh (או"ח ס' קמו ס"ק ד), despite ruling it unnecessary to stand, writes that if someone does want to accept the practice of the Maharam, we should not discourage him.
The Tur (שם ס' קמו) quotes Rav Sar Shalom who says that one does not have to stand except for the taking out of the Torah and its return to the Aron, until the congregation answers יהא שמיה רבא, after the reading of the Torah. The Beis Yosef (שם ד"ה כתב רב), in quoting Rav Sar Shalom and the Ba'al HaManhig who likewise quotes him, writes that whoever stands from the taking out of the Torah until its return is making a mistake in translating the Posuk in Nechemiah. The Bach (שם ד"ה כתב רב) explains that even Rav Sar Shalom admits that one must stand while the Torah is being taken out, and only then may he sit, only to have to stand again for its return to the Aron.
The Chayei Adam (כלל לא סע' ג) rules that one may sit while the Torah is being read because it is not moving, but when it is being moved one must stand, such as during Hagbaah and while it is being carried to and from the Aron. The Sha'ar HaTzion (שם), commenting on the Mishnah Berurah, writes that even though technically one does not have to stand during Hagbaah since the Torah is in another domain, one must stand because the only reason why it is being lifted is to show it to the people. The Aruch HaShulchan explains that one would technically not have to stand during the reading because the Sefer Torah is resting on the Bimah, and one only has to stand when it is moving. After quoting the Vilna Gaon, the Pri Chodosh, and the Bach, the Mishnah Berurah (שם אות יט) writes that if someone is weak, making standing difficult for him, and he therefore can not concentrate on what is being read, he should sit down. Seemingly, the Mishnah Berurah would say that if someone is able to stand he should, even if technically he does not have to do so.
It should be noted that even according to those who say one need not stand during the reading of the Torah, it seems universally accepted that one must stand for the Barchu that precedes it. The reason for this being that Barchu is a דבר שבקדושה, a holy matter, which requires one to stand. The Magen Avraham (שם), the Taz (שם), the Be'er Heitev (שם), the Mishnah Berurah (שם אות יט), the Chayei Adam (שם), and the Aruch HaShulchan all rule this way. It should also be noted that even according to those who do take it upon themselves to stand for the reading it seems that between Aliyot it is not necessary to stand. The Be'er Heitev (שם ס"ק ו), the Pri Chodosh (שם), the Aruch HaShulchan, and the Mishnah Berurah (שם אות ה) all rule in this manner.
HaRav Joseph B. Soloveitchik (שעורים לזכר אבא מרי ח"ב ר"י-רי"ג) writes that our reading of the Torah should be identical to the experience of standing before Hashem at Har Sinai. One should relive the experience of the thunder and the sound of the Shofar which were all present at Har Sinai, and he should picture that the reading of the Torah is coming from Hashem Himself. He also compares it to Har Sinai in a different light. The Rambam (הל' תפילה פ"ח ה"ד) writes that we do not say Kedusha or read the Torah unless there are ten people present. The connection between Kedusha and reading the Torah is puzzling. However, Rabbi Soloveitchik writes that the reading of the Torah is comparable to Har Sinai experience also in that both are קבלת עול מלכות שמים, an acceptance of Hashem as our God. Like any acceptance which requires ten people, the Torah reading is transformed into a דבר שבקדושה, a holy matter. It is for this reason that the Rambam places Kedusha and the Torah reading next to each other because they are both דברים שבקדושה.
The fact that one must stand for a דבר שבקדושה, as mentioned above regarding Barchu, is subject to debate. The Ramo (או"ח ס' נו סע' א) writes that one should stand for any דבר שבקדושה, while the Magen Avraham (שם ס"ק ד) quotes both the Maharil and the AriZal who ruled that one does not have to stand. However, since we do follow the position of the Ramo, and in light of how Rabbi Soloveitchik classifies the reading of the Torah, it seems that one must stand while the Torah is being read, like any דבר שבקדושה. However, it is reported that Rabbi Soloveitchik did indeed say that what the Maharam did was a stringency (ספר בית יוסף שאול עמ' 102-002 הערה 6), and that standing is not mandatory. Rabbi Hershel Schachter (נפש הרב ליקוטי הנהגות או"ח עמידת הקהל בשעת פתיחת ארון הקדש) presents a reason why one need not stand even though the reading of the Torah may be classified as a דבר שבקדושה. A דבר שבקדושה is any praise that is said not in the form of a Beracha or a Posuk. The Gemara in Berachos (י:) presents the opinion of Beis Hillel who says that one can read שמע in any position based on the Posuk ובלכתך בדרך. If one wants to classify the Torah reading as a דבר שבקדושה, perhaps the requirement to stand is waved off because of this special derush, something learned out, in the Gemara in Berachos. If this is the case one can also say, Rabbi Schachter writes, that the requirement to stand for Barchu can be waved. Despite it being a דבר שבקדושה, once we classify it as part of the Torah reading, it should take on all the laws of the actual Torah reading, thus making it also unnecessary to stand for Barchu.