hotcoldhot:
Well, a portion of the Torah (meaning, specifically from the five books of Moses) is read from a parchment scroll in synagogues during morning prayers on Mondays, Thursdays, Sabbath (Saturdays), holidays, fast days, and the beginning of every month (on the Hebrew calendar),and during afternoon prayers on Sabbath and on fast days. Most congregants will follow the reading in a Chumash (described earlier in this thread), or in a prayer book - called a Siddur, or on Holidays, some use a specialized siddur called a Machzor - which has the day’s Torah portion printed therein.
Portions from the books of the Prophets (Joshua, Judges, Samuel, Kings, Isaiah, Jeremiah, Ezekiel, and the twelve minor prophets - Hosea, Joel, Amos, Obadiah, Jonah, Micah, Nahum, Habakkuk, Zephaniah, Haggai, Zachariah, and Malachi) are read after the Torah portion on Sabbath and holiday mornings, and on the afternoons of Fast Days, plus on the morning of the ninth of the Hebrew month of Av, a very special fast day. (Yom Kippur counts as both a holiday and a fast day.) Some synagogues have these on parchment scrolls as well, but in most, these portions will be read from a Tanakh. The congregants will likely follow along in the same book which they followed the main reading in, those usually have the appropriate prophetic portion in there for convenience.
On five occasions during the year, a book from the Writings is read - Esther on Purim, Song of Songs on Passover, Ruth on Shavuot, Lamentations on the ninth of Av, and Ecclesiastes on Sukkot (or the day after Sukkot, which is technically a different holiday, albeit adjacent). Just about any synagogue will have Esther in parchment scroll form, but the other four are, like the prophetic books, not so common for synagogues to have as parchment scrolls. Those that do have them will read from them, those who don’t will use a Chumash or Machzor or Tanakh. The congregation will generally follow the reading in a Chumash, Machzor, or a printed book of that reading, but on Purim, many congregants will have their own parchment Esther scrolls.
Daily prayer services include many scriptural passages, mostly from Psalms, some from the five Books of Moses, and a bit from Chronicles and Nehemiah. These will be read from a Siddur (or Machzor, on holidays), as that book has all prayer services arranged in the proper order for prayer. The Passover ritual is conducted witha Hagaddah, which similarly includes scriptural passages and is arranged in the order required for ritual.
Psalms will also frequently be read in times of trouble, or as part of memorializing the dead. A dedicated book of Psalms (separate from the rest of Tanakh) will usually be used for this; the cover of this book would read, in Hebrew, “Tehillim.”
Torah study is greatly encouraged in Judaism, though the majority of those engaging in free study will learn Talmud rather than scripture. However, those who do spend their time learning scripture could certainly be learning it from a Tanakh.