The Quest For Greatness can be accessed via the Experience PlayStation 4 area, which is connected to the Home main hub. Inside the Experience PS4 area is a giant PlayStation Vita, and it is here your quest begins. Reddit posters have claimed that the ordeal shouldn't take more than roughly 10 minutes, so if that amount of time for three PSOne games playable on your PS3 and Vita sounds worth it, log onto PlayStation Home and get to collecting.
Via: Polygon
Source: Reddit