Finding a webdesigner can be easy or hard, the first thing you need to ask yourself is whether you are looking for a company, or a freelancer to do take up your project.

Each have advantages and disadvantages, you just need to feel at ease with whoever you choose.

www.yaxay.com is full of talented freelance designers

I would also recommend designoutpost.com, this is a forum for design contest where only those individuals selected for the design team can particpate. The benefit of this forum over yaxay is.....you are always guaranted an honest business transaction, due to the nature of the website.

Well, the average person/company is known to statistically go off word of mouth. It's always

"Hey Chris, we need a new site so if you know anyone, have them call us"

"Actually John I do, I have this friend who is learning to design and could help us out."

It depends on your pricing. If you are charging well in the thousands, then your best bet would be to simply hire a marketer for your studio, to actually go out and contact people both in the city that your studio is located in, but to also submit emails of websites that could be a potential client. Hiring someone to go out and do the research to see who needs what, and how much they're willing to put up for that could be a very rewarding decision.

Small budgeted companies go by word of mouth, or who they know of in their city.
Companies with large budgets specifically for the web go to websites of studios who they know have the ability and experience to get what they want WHEN they want it (another important factor.)