Under the current Code of Canon Law (1983), two miracles are required for someone to be canonized as an official saint. The first miracles results in beatification, then the second one in canonization. Prior to that, canon law had quite a few more requirements, and I think more than two miracles (IIRC). As a result, canonizations prior to 1983 were few and far between, whereas its become more common since then. I'm not sure what I think of that, to be honest.
Of course, it gets a little more complicated, as the pre-1983 canon law has it own predecessor practices. In the first 1100 years or so of Church history, the canonization of saints was more by popular acclaim. That is, a holy person would die, people would pray to them and seek their intercession, and if they could work miracles for their followers, then their following grew and would eventually be recognized by the local bishop. But toward the end of the 1100s, canonization was reserved exclusively to the pope. This largely grassroots canonization process still continues, officially unrecognized, as the veneration of Fr. Villars and many other folk saints demonstrate.
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Of course, it gets a little more complicated, as the pre-1983 canon law has it own predecessor practices. In the first 1100 years or so of Church history, the canonization of saints was more by popular acclaim. That is, a holy person would die, people would pray to them and seek their intercession, and if they could work miracles for their followers, then their following grew and would eventually be recognized by the local bishop. But toward the end of the 1100s, canonization was reserved exclusively to the pope. This largely grassroots canonization process still continues, officially unrecognized, as the veneration of Fr. Villars and many other folk saints demonstrate.