On Shabbat in Orthodox, Conservative and Hasidic synagogues, the procedure for reading Torah is mostly uniform. (I’ve attended Reform services on some Friday nights but rarely on Shabbat morning, so I can’t fairly state what procedure is followed there.)
In the traditional settings, the Shabbat Torah reading is divided into 7 sections (the number varies on holidays and weekdays). The reading of each section is preceded by a congregant being called up to say the brachot/blessings before and after the reading.
Being called up is an honor, called an “aliyah” — a Hebrew word meaning “up” or “going up.” The same word is used for a Jew who moves to Israel. It’s referred to as “making aliyah.” Why? Metaphysical meanings aside, it’s based on the historical pilgrimage to the Temple in Jerusalem, which sat atop Mt. Tzion. To get there, one “went up” the mountain.
We might also recognize it from the Israeli airline “El Al” — “To (the) Above.”
After the opening blessing is said, the specified section of Torah is read by a trained reader called a “ba’al koreh” — which roughly translated means “the person who has mastered reading.”
What is there to “master?” In a sefer Torah, the Hebrew is written without vowels or punctuation marks. The reader must literally memorize the reading. This is done using a manual called a “tikkun.” In it, each Torah reading is presented in two columns: one with the vowels and punctuation, the other without. The procedure is to practice by repeating a sentence or even a few words, reading from the voweled/punctuated column; then read the same sentence from the unvoweled/unpunctuated column. Repeat until the entire week’s reading is memorized.
The voweled column also displays the “trop” marks, which indicate what musical motif to use for each word. This, too, has to be memorized. The trop marks also indicate phrases and pauses. After I had done this for a while, I began to see the general pattern and could reasonably anticipate what mark/trop would be used — especially in shorter sentences. The trop marks also sometimes clarify the correct syllable on which emphasis must be placed. In this case, it corresponds more to Sephardic than to Ashkenazic pronunciation. In Sephardic pronunciation, for example, the emphasis is almost always on the final or “ultimate” syllable; in Ashkenazic, on the “pen-ultimate” syllable — i.e. the one preceding the final syllable. A good example of this is the pronunciation of “Shabbat:” In Sephardic, it’s Sha-bát; In Ashkenazic, it’s Shá-bis. The trop conforms more to the Sephardic pronunciation.
The chanting or “cantillation” of Torah is also not meant to be an “aria” as much as a “recitative.” Torah is being “spoken” or “proclaimed,” with musical aspects used to enhance the speaking by providing some variation, indicating pauses, phrases and stops, and generally making the proclamation more interesting than a monotone reading would be. Having done it many times, I’d say that it also helps get the individual will out of the way because everything is prepared in advance; the act itself, like art and performance, can then flow more freely.
Preparing a weekly reading can take 15-20 hours of work, even for an experienced reader. I was once offered a job with a large congregation that involved reading Torah and teaching many bar/bat mitzvah students. I turned the job down, because I realized that I would literally never have a day off. Even on a day when I wasn’t scheduled to see students, I’d have to be working on that week’s Torah reading. I didn’t think I wanted that much pressure.
Nowhere is the above procedure mentioned in Torah itself. Instead, like many religious customs, it evolved over time. There was a time, for example, when the schedule of weekly readings itself wasn’t standardized. One might begin anywhere. There was probably also no set number of “aliyot” (plural of “aliyah”). There was certainly no fully standardized “trop” until around the 9th or 10th century (although this finalization grew, as always, out of what had preceded it).
In ancient times, there also seems to have been a “triennial” cycle of reading Torah — i.e. it was divided into weekly readings that took 3 years to complete. We don’t know the exact places where each weekly reading started and stopped at that time, but in recent years, the Conservative movement has tried to offer a triennial cycle as an alternative to the typical annual one. This has the advantage of shortening each reading and the corresponding time it can take to prepare it. It also shortens the amount of time that reading Torah can take during the service, without reducing the number of aliyot and offers — ideally, anyway — the chance to give more attention to the smaller selection of verses each year. I have no idea how widespread (or not) this has become, but it’s a good alternative, depending on the needs and tastes of the congregation.
Another alternative — less popular but generally acceptable — is for someone to read the aliyot from a chumash (which contains the trop and vowels) while another person follows the reading in an open sepher Torah. Once, while serving as rabbi for a High Holiday service, I read from the chumash while the cantor, from across the front of the room, followed in a sefer Torah. We invited the children to come up and stand with the cantor, to see what a Torah looks like “inside” and experience what he did with the pointer. I thought it served an excellent educational purpose.
It’s also possible that the Shabbat reading wasn’t always from Torah, either! An episode from the Gospel of Luke is an example of this:
“[Jesus] went to Nazareth, where he had been brought up, and on the Sabbath day he went into the synagogue, as was his custom. He stood up to read, and the scroll of the prophet Isaiah was handed to him…” 
To a contemporary Jew, this would seem very odd.
Why was the “scroll of the prophet Isaiah” handed to him? Because the readings weren’t yet standardized. In this case, it seems that Torah itself might not even have been being read; a section from “Isaiah” being read instead (unless this reflects a “haftarah” reading, which I’m not sure even existed at that time).
Who chose that scroll for Jesus to read? This anecdote doesn’t say. It might have been the rabbi, the gabbai or some other synagogue functionary. It might even have been Jesus’ own request.
It wasn’t until some time later that the weekly/annual cycle of readings was put into place (which varies in Ashkenazic and Sephardic tradition even today).
But there’s another major difference between the past and the present:
In ancient and early medieval times, the person given the aliyah also read it!
Thus, instead of a trained ba’al koreh, each member of the synagogue read his own section (women were never called up in those days).
I think that explains why an “aliyah” was such an honor: the person called was instructing the entire congregation in a portion of the text of Torah! It might also imply that the person who was doing the reading had studied some commentary in addition to preparing the reading itself – so to read was also to learn!
By the Middle Ages, the number of people skilled enough in Hebrew and reading Torah was so diminished that “professionals” had to be created — thus, the “ba’al koreh” emerged!
As mentioned above, reading Torah requires considerable skill and time. One would think that it would be a well-paid profession, but this is not at all the case. A ba’al koreh is paid very poorly — probably because the congregation doesn’t give as much respect to the simple reading as it does to the rabbi’s interpretation of or sermon on the parshah. I don’t think most people realize how much work is involved. It looks so easy! In many places, the poor payment of a ba’al koreh is moderated by the responsibility being designated to the cantor — a generally better-paid role.
Once, on Manhattan’s West Side, I even saw an example of a ba’al koreh who read in multiple synagogues on the same day. This was possible because there were so many synagogues in a close area and there was some variety in what time Torah was being read in each one. He could easily get from one to another. So, a ba’al koreh who was being paid $50 for reading, might make $200 for doing the same reading in 4 different places — with no additional preparation time! On the Shabbat morning I saw this, the ba’al koreh was late! Apparently, there was some delay in one of his early “appointments” (possibly they were waiting for a minyan in an early-morning service), causing a back-up in each subsequent congregation! We literally reached the end of the Shachrit (Morning) service and waited! The ba’al koreh couldn’t call anyone, of course — it was Shabbat!
In Orthodox synagogues, the bimah (raised platform) from which Torah is read is in the middle of the synagogue chapel. Torah is read facing the aron/ark, but with the congregants in seats surrounding the bimah. One of the innovations of the Reform movement was to move the “bimah” to the front of the chapel. Many Conservative synagogues follow the same layout.
The problem (for me) arises when Torah is read from a bimah in front of the room, but with the reader still facing the aron/ark. It’s supposed to be informing and instructing the congregation, but in this case, the “teacher” is teaching with his back to the class!
The reader is accompanied on the bimah by the gabbai and another person checking on the reader’s pronunciation (there must always be 2 witnesses!), plus the person who is receiving the aliyah. The person who receives the aliyah remains on the bimah until the end of the subsequent aliyah — so there are 5 people on the bimah involved in the Torah reading, all with their sides or backs facing the congregation — i.e. the audience for the reading. Not good pedagogy or even theater.
I far prefer those congregations who, having moved the bimah to the front of the chapel, read Torah facing the congregation.
For public reading, a sefer Torah is placed on a shulchan/table — the same one from which prayers are said while facing the ark. The shulchan can be slightly inclined to make it easier for the reader. One congregation I visited years ago had a lever on the shulchan. When the cantor was leading prayers, the shulchan faced the ark. When it was time to read Torah, the lever was pressed and the shulchan manually rotated to face the congregation! Then, when it was time to do Musaf — the service after reading Torah — the lever was pressed again and the shulchan rotated back to face the aron/ark. Clever!
In a chavurah that I attended for a few years many years ago, the shulchan was an actual, movable table. My memory is that it was placed in the middle of the room when prayers were being said/led, then manually moved by several people to the front of the room for reading Torah; then back to the middle again for Musaf. It was a post-’60’s ambience; moving the table manually and cooperatively fit in perfectly with the communal and informal ethos of the times. It didn’t hurt that we were in our 20’s and 30’s, rather than our 60’s and 70’s, either.
All this being said, there’s something magical about being in a room when Torah is being read. When no Torah was available, I’ve sometimes had to conduct a service by reading from the chumash alone. Something is definitely missing. In one nursing home, I tried to make up for this by buying small sefer Torahs, like the ones that children carry on Simchat Torah. It was the best I could do under the circumstances, but it certainly didn’t make up for the absence of an actual sefer Torah.
For those reading this piece, I suggest that you might deeply enjoy learning to read Torah with trop. Even if you never read in front of a congregation, it will be a deep experience just doing this on your own, in your home.
 Luke 4:16-17