Short answers, pulled from the story.
The Seljuk Sultan Alp Arslan defeated the Byzantine Emperor Romanos IV Diogenes on the 26th of August 1071. The battle involved a Seljuk crescent formation that surrounded and routed the Byzantine army through Parthian tactics.
Alp Arslan led the Seljuks to victory over the Byzantines in 1071 after capturing the city of Ani in 1064. Romanos IV Diogenes was captured by Alp Arslan following the defeat at Manzikert.
The main engagement occurred on the morning of the 26th of August 1071 near Khnus city. Romanos had captured Manzikert easily on the 23rd of August before facing attacks from horse archers the next day.
Steven Runciman called it the most decisive disaster in Byzantine history lasting seven and a half centuries. The defeat created a power vacuum that allowed Turkic migrations to fill Anatolia and establish their capital in Nikaea in 1077.
Modern scholars estimate Byzantine losses were relatively low since many units survived intact despite heavy casualties among the emperor's personal troops. Anna Komnene wrote that later sources greatly exaggerated troop numbers and casualties following the battle.