The stoning schedule varies by day. On the 10th of ذو الحجة (يوم النحر / Day of Sacrifice), only الجمرات al-Aqabah (the largest pillar, closest to مكة) is stoned. The time begins after midnight عند the Shafi'i and Hanbali schools, or after Fajr عند the Hanafi school. The السنة is to stone it after sunrise but before Dhuhr. Stoning on this day should ideally be completed before sunset, though most scholars allow it to continue until Fajr of the 11th if necessary.
On the 11th, 12th, and 13th of ذو الحجة (Days of التشريق), all three pillars are stoned in sequence. The time for stoning on these days begins after the sun passes its zenith (zawal / Dhuhr time) عند جمهور العلماء. The Hanafi school allows stoning before Dhuhr on these days, but the majority position is after Dhuhr. Stoning should be completed before sunset, though the Hanafi and some Hanbali scholars permit stoning until Fajr of the following day.
To avoid the most dangerous crowd crushes, consider stoning during off-peak hours. The period immediately after Dhuhr on the 11th and 12th tends to be very crowded. Later afternoon (between Asr and Maghrib) or early afternoon are often better. Many scholars now allow stoning after sunset due to the enormous crowd sizes, prioritizing الحاج safety. Follow the guidance of your الحج group leader and the Saudi authorities, who implement crowd control measures and designated timing slots.