How hard is it really to find a rental apartment as a newcomer?

My rental contract in Utrecht ends in December and I am starting to stress about it. I have been in the Netherlands about two years. Until now I rented a room from people I know, so I never did a real housing search. Now I need my own place, and everyone tells me something different.

What I understand so far (please correct me):

• For social housing people say the waiting lists are many years, so realistically it is not an option for me right now. I registered anyway to build up waiting time — was that smart?
• In the free sector, agencies seem to ask for an income of 3 or 4 times the rent. With a part-time salary that feels impossible alone.

My questions for people who did this recently: how long did your search take? How many viewings before you got a place? And how do you recognise scams — I heard you should never pay anything before you have seen the apartment and the landlord in person, is that the main rule?

Please tell me it is doable. I am trying to stay positive, but the stories scare me a little.