How was Mathias chosen as an Apostle?

After Jesus ascended into heaven, the 11 apostles wanted to replace Judas Iscariot, who was dead, with someone else who had been with them the whole time Jesus had been among them. So they came up with two men: Joseph called Barsabbas and Matthias, and they prayed, cast lots, and chose Matthias. This account is given in detail in Acts 1:12-26.