The stoning sequence differs between the Day of Sacrifice (10th) and the Days of Tashreeq (11th-13th). On the 10th of Dhul Hijjah, only one pillar is stoned: Jamarat al-Aqabah (also called al-Kubra — the largest pillar, located nearest to Makkah). You throw 7 pebbles at it, saying 'Allahu Akbar' with each throw.
On the 11th, 12th, and 13th of Dhul Hijjah, all three pillars are stoned in a specific order, starting from the one farthest from Makkah and moving toward Makkah: (1) Jamarat al-Sughra (the smallest, farthest from Makkah) — 7 pebbles; (2) Jamarat al-Wusta (the middle pillar) — 7 pebbles; (3) Jamarat al-Aqabah / al-Kubra (the largest, nearest to Makkah) — 7 pebbles. This order is wajib (obligatory) according to the majority of scholars.
The Sunnah after stoning al-Sughra is to move to the side, face the Qiblah, raise your hands, and make a lengthy dua. Similarly after al-Wusta — stand, face the Qiblah, and make dua. However, after stoning al-Aqabah (the final pillar), you do NOT stand for dua — you simply leave the area. This follows the exact practice of the Prophet (peace be upon him). The modern Jamarat bridge is a multi-level structure designed to ease crowding — you may stone from any level, and the pillars are now wall-shaped (not actual pillars) with a basin to catch the pebbles.