Based on my experience, people have no idea where to turn. they start asking around through business contacts, friends, family, etc..
This is where the whole notion of "I have a nephew that can do this work for me" comes from. People ask around until someone they come across says "I know a little about web design" and they just go with that person because they don't understand the implications.
Once people start getting serious about their web needs, they start asking the right questions. Instead of looking for someone who "can build [me] a website" they start looking for someone who understands their business needs. Unfortunately, this only tends to come about after a failed project with the "nephew".
Once they get to this point and understand that a strong website can make or break a business, they start to understand the value and start looking for professional firms.
Again, this has been my experience dealing with local clients. I'm sure it's different in other cities.