The genre developed in the medieval period (~10th-14th centuries). Some zemirot are by named authors with surviving acrostics: Avraham ibn Ezra, Yehuda HaLevi, Yisrael Najara, Shlomo Alkabetz, and others. Many are anonymous medieval folk compositions that entered family use through unknown channels. The Spanish-Sephardi tradition has the richest written corpus; the German-Ashkenazi tradition often preserved zemirot orally before they were eventually printed in the 16th-17th centuries.
The melodies are even more varied than the texts. The same lyric is sung to different tunes in Yemen, Morocco, Poland, Iraq, Italy, and Spanish-Portuguese communities. Modern Israeli versions often combine Carlebach-style chant with Mizrahi elements.
Practically, zemirot do several things:
1. Mark transitions in the meal. After each course, a zemer signals "we're still at Shabbat dinner, not at an ordinary meal". The singing extends the meal and stops it from becoming purely transactional.
2. Teach children. Children pick up zemirot by ear over years of Shabbat meals. By the time a Jewish child is 10, they've heard Tzur Mishelo 500 times. The melody and words are knit into early memory.
3. Anchor mystical themes. Friday night is, in the kabbalistic tradition, the marriage of the Shechinah (feminine divine) and the Holy One. The zemirot frequently use language of bride/groom, attraction/embrace, mystical union, kept gentle enough that children sing them without noticing the depth.
4. Lengthen Shabbat experientially. The meal extends to 2-3 hours. Conversation slows. Songs are interspersed with stories, divrei Torah, jokes. By the end, Friday night has felt distinct from any weeknight dinner.
The standard reference: any bencher (small printed booklet) sold in any Judaica shop, typically contains Birkat HaMazon plus the 12-15 most common zemirot. Many families have a stack of benchers customized for a specific wedding or bar/bat mitzvah; these become collector items. Online: Sefaria has the full corpus of Shabbat zemirot with translations. YouTube has dozens of recordings of each major zemer in various rite-melodies.
The fastest way to learn: spend a Friday night with a family that sings them. After 3 weeks of regular attendance, you'll have the refrains of Tzur Mishelo, Yom Shabbaton, and Yah Ribbon by heart, and the rest follow.