Upon arriving at Muzdalifah after sunset from Arafah, the first priority is combining Maghrib (3 rak'ahs) and Isha (shortened to 2 rak'ahs) shalat. Nabi (shallallahu alaihi wa sallam) combined these two shalat at Muzdalifah with one adhan and two iqamas. This should be done soon after arrival — do not delay the shalat unnecessarily to settle in.
The requirement for staying at Muzdalifah varies by school. The Shafi'i and Hanbali schools consider staying at Muzdalifah even for a moment after midnight as fulfilling the wajib (wajib act). The Maliki school requires staying most of the night. The Hanafi school considers the stay at Muzdalifah as wajib, and departing before Fajr without excuse requires fidyah. The strongest practice is to stay from arrival until after Fajr shalat, then depart for Mina before sunrise — this is the Sunnah of Nabi.
During the night, collect 49 pebbles (or 70 if staying in Mina for 3 days of Tashreeq) for the stoning ritual at Jamarat. Pebbles should be slightly larger than a chickpea. Sleep under the open sky — there are no tent structures at Muzdalifah. Make doa and dhikr, especially at the Mash'ar al-Haram area. The night at Muzdalifah is a profound spiritual experience of simplicity and equality, as all jamaah haji — rich and poor — sleep on the bare ground together.