Never shop on price:
Whilst you don't always get what you pay for. You almost never get what you expect if you aren't willing to pay properly for it.
Pay careful attention to the portfolio of the website designer:
What they have done is a good indication of what you will get. In addition, look at the web designer's own website. Avoid web design companies that still use flash introductions on their own website.
Give a small project first:
If you plan to spend a lot of money with the company, try giving them a small project first. If their service and quality of product is what you expect, they will deliver on their promises and you can move onto bigger things with that company. If they don't deliver, then you haven't wasted huge sums of money.
ALWAYS define exactly what you need before the project begins:
Like it or not, a project plan with specifications is going to save a lot of trouble later on, both for you and the design company. The specifications do not have to be four hundred pages long, but they should define any important features that could otherwise be ambiguous.
Meet the team:
Have a conversation with the project manager and make sure that you get to speck to the whole team that will be working on the site or at least meet them. A good project manager should be able to convey your requirements to the team properly, but good project managers are uncommon. You'll be safer if you can have a chat to everyone involved in one meeting. Getting everyone to take notes and thus ensuring that the team as a whole has an understanding of what you are trying to accomplish; straight from the horse’s mouth.
Ask for references and/or testimonials:
This may or may not be possible depending on the web design company. But if they are more than willing to let you speak to other clients, then more than likely their previous clients like them, which is a good sign.
The level of due diligence that you perform on the company should of course be kept in check with the size of the job you intend to have them do for you. If you are getting them to do a $250 online greeting card, getting 10 references, having 4 prior meetings and asking for a 100 page specification is likely going to cause you to be tossed aside in favor of a client that is worth the trouble. On the other hand, if you are having them build the next major shopping portal for you group of 185 country-wide chains of stores and plan to have it integrate with the services of several large companies, be absolutely sure the web design company knows what they are doing and has experience doing it. You don't want a company that is learning the ropes by using you as a guinea pig.