When: after a meal where you ate bread (at least a kezayit, about the size of an olive). The Torah commands it: “You shall eat and be satisfied, and bless Hashem your God for the good land He has given you” (Devarim 8:10 · Direct Source). The Talmud says the blessings were set by Moshe, Yehoshua, David and Shlomo, and the fourth by the Sages at Yavneh (Berachot 48b · Direct Source).
How: sit where you ate. On Shabbat and Yom Tov, begin with Shir HaMa’alot (Tehillim 126). With three or more men who ate together, one leads the zimun (the invitation) first. Special days add a paragraph inside: Retzei on Shabbat; Ya’aleh V’yavo on Yom Tov and Rosh Chodesh; Al HaNissim on Chanukah and Purim — they are marked in the text.
The whole Birkat Hamazon — every wordHebrew · transliteration · English · Hear it
After cake, pasta, wine or the special fruits (grapes, figs, pomegranates, olives, dates), the short after-blessing is Al HaMichyah; after everything else, Borei Nefashot — see Blessings.