Families sometimes tried to arrange the matches, but sometimes women took their chances because they could not escape their past - be that broken engagements or the death of parents from TB. They married a man whose picture they saw and whose family or friends vouched for him. Sometimes the picture sent was old or of someone else, more handsome. The estimate is that about 20,000 women came to Hawaii and married as picture brides, and this DVD that I'm highly recommending is the fictionalized account of one woman. The film is beautiful artistically as well as interesting.
Hawaiian genealogy is becoming easier. Because the Hawaiian islands were annexed by the United States in 1898 there is actually census US FEDERAL starting in 1900, and at first the count was by ISLAND. Once Hawaii became part of the United States, counties were established and the counts went by county. Ship records are also available.