The amount of time it takes to design and develop a website depends on two things: the web designer, and the client. With a fast web designer and a responsive client, the website will be completed very quickly. With any other combination, results will vary.
Assuming a small to mid sized website of 15-25 pages, here is what you can expect.
On average, figure 4-8 weeks to complete your web design project. This assumes that the web designer offers good customer service, and the client provides a reasonable response time. A large portion of this time is spent by the client getting the necessary content for the entire website.
Completing the site in 3-4 weeks is considered fast. In this case, you have a web designer that is fast, and you have a client that is completely prepared and has all the content ready to go.
Some web design projects drag out for months. In some cases this may be due to a web designer that is very busy, or just not very responsive. In other cases this is due to the client not having the time or resources to spend on developing the content for a website.