I wrote an answer to a similar question you might be interested in. Find it here.

The long and short of it is that they had to know someone. Not necessarily someone willing to hide them, but just someone who was involved with resistance activity in any form (and there were LOTS of types, some of which had little to do with hiding Jews, but all of which put people in contact with other resisters). From there, it was a matter of introductions that were not entirely dissimilar to those portrayed in the movie Goodfelles about mafioso, wherein a mutual person of trust would introduce two new people, assuring both parties the other can be trusted. The person in need of help would then sort of move down the line until they were able to find someone. There are lots of stories of folks going from place to place to place for a few days or weeks, waiting for a more permanent hiding spot, staying one step ahead of the authorities.

I should note that it certainly didn't hurt if you had a lot of money to pay for help. While many people hid Jews or participated in resistance activities out of conviction, it wasn't uncommon for folks to participate out of greed. I can think of one published account in which a Jewish family in the Netherlands paid another family for shelter during the occupation. That family was not terribly interested in helping the Jewish family, but they were interested in the Jewish family's money. The helper family also participated in black market activities, much to the consternation of the Jewish family (that put the Jewish family at much higher risk, should the one of the helpers get caught in unrelated illegal activity).