One of the difficulties in having a web site designed for you is that you may not know what to look for. A way to get around this is to ask for explanations... in writing.
For example, you may have a web designer come up with a look for your site. Make sure you ask for a written description of this look. This is called a style guide. A style guide may relate to the combination of colors on a site, each page's layout, the feel of the writing on the site, or all of the previous. The style guide itself may be online, in electronic form, or even a physical booklet. The style guide will not only help you understand the work that is going in to developing your site, it is also a very valuable resource. A style guide allows someone who has never worked on you site before to edit your current pages and add new pages to your site while maintaining the look and feel of the overall website. This guarantees that your site will not only look good the first day it goes live, but that your site will continue to look good after years of edits and updates.