Question: How did the Stations of the Cross begin?
Bonus question: What does "Via Dolorosa" mean?
Answers: The Stations of the Cross have evolved over time, but started soon after Jesus' crucifixion and resurrection. The Blessed Virgin visited the scenes of Christ's Passion daily. Later, pilgrims visited these sites/stations. Eventually, reproductions of the stations were allowed in churches for the purpose of practicing the devotion as if on an actual pilgrimage to the holy land.
Follow this link for an easy to read article on the history of the Stations of the Cross:
http://catholiceducation.org/articles/religion/re0089.html
Via Dolorosa generally means "Way of Sorrows" and refers to the path through Jerusalem where it is believed that Jesus carried his cross on the way to crucifixion.