M.S.
The price range and the method of charging can vary greatly between designers, just as their specialties can vary greatly. Before becoming a mom I used to have a small interior design business. I charged by the hour for shopping, painting, design time, etc for some jobs and for others I gave them a flat quote for time and materials. It really depended on the job I was doing and the client's needs.
First, make sure they offer a free consult to come to your home and let you know what they can offer. While talking on the phone give them an idea of what you are looking for and your budget. You will know if they are in your ballpark this way. Remember, just because they come to your home for this consult you don't have to hire them. It is just to see if they are a good fit.
You can find a designer on line, in the phone book, or better yet, by word of mouth. Do you have any friends' homes that you absolutely love? Ask them if they used a designer-- or maybe they have great taste and may want to help you themselves.
Or you could find one at a furniture store or design center that you love. You may receive a discount on their merchandise or free design service this way. The catch here is that they will be pushing their own stuff.
Remember, designers have to make money too, so you will be paying extra for their knowledge, experience and sources, but if you don't know where to start, if could be very beneficial in the end. Not to mention saving you the leg work and headaches!