As a web designer I naturally look to create eye catching websites with understated, sleek layouts. When thinking about the design of your website you need to look at it from two viewpoints. The first is layout & accessibility, the second is style & beauty. You will want your design to strike a harmonious balance between practicality and glamour, so that it looks good and is easy to use.
By this point you should have at least an idea of how many pages you need and how to divide your website up into sections. You need to think about a navigation structure, by which your pages include hyperlinks to other relevant pages within your website. You may want your pages to have a common header & footer to maintain consistency across the site. You may want a navigation bar or links menu in the header or footer. You may end up with a 'web' of links from page to page, or you may have enough content to justify a hierarchial navigation structure. Think about what would be easiest for the visitors you care about. The website users should be able to find what they are looking for easily and quickly, and your design should not alienate your target audience.
Next you think about what kind of tone you want your pages to strike with the viewer. Bright and fanciful? Monotone and simple? Based around a particular colour? The purpose of your website should be conveyed in its design and this may impose some design constraints. Think back to your target audience and find out what kind of look they would appreciate. Corporate, fun, official, modern, etc. The deeper you go with this, the better for the designer. You should think about fonts, images, borders, backgrounds, links, etc.
As a rule of thumb, greater detail in your design plan is good for everyone involved. It is better (and cheaper!) to communicate your detailed design plans to the designer right from the start, than to give the designer a lackluster general brief and later have parts redesigned. It is of course up to you to decide how much work you want to do. Leaving the design entirely to the designer is a gamble - you may get something that looks great, but doesn't match up to the target audience of your website.