The weekday Amida has 19 blessings in three sections:
Praise (3 blessings): 1. Avot (this page) → 2. Gevurot (God's might, especially in resurrection) → 3. Kedushat HaShem (sanctification of the Name, including the Kedushah during chazan repetition).
Petition (13 blessings): knowledge, repentance, forgiveness, redemption, healing, livelihood, in-gathering of exiles, restoration of justice, against slander, the righteous, Jerusalem, Davidic kingship, the hearing of prayer.
Thanks (3 blessings): 17. Avodah (acceptance of worship) → 18. Modim (thanksgiving) → 19. Sim Shalom (peace).
On Shabbat and holidays, the 13 petition blessings are replaced by a single "holiness of the day" blessing, so Shabbat Amida has 7 blessings total. The reasoning: Shabbat is rest from struggle; one should not petition for needs but accept the peace of the day.
The name Amida means "standing", the worshiper stands during the entire prayer. The standing posture comes from the Temple service: priests stood; the people stood. The silent voice (no audible sound) comes from Hannah's prayer at Shiloh (1 Sam 1).
Some communities have the Amida said aloud once ("chazan's repetition") after the silent recitation, so the people who can't read fluently can fulfill their obligation by listening. This repeated version includes the Kedushah (sanctification with the angels) and Modim D'Rabbanan (the people's parallel Modim during the chazan's Modim). Both are public additions; the silent Amida has neither.
Before saying the Amida, the worshiper takes 3 small steps backward then 3 small steps forward. The Talmud (Berachot 26b) attributes this to courtly etiquette: when approaching the King one steps back to show the space being entered. The three steps also recall the three sections of the Temple (outer court → inner court → Holy of Holies), through which the High Priest progressed only once a year on Yom Kippur. Now every Jew passes through this approach three times a day.
At the end of the Amida (after the closing blessing of Sim Shalom), 3 steps backward again, to take leave of the King. Then bow left, right, and forward saying Oseh Shalom bimromav ("He who makes peace in His high places...").