How important is it for a graphic designer to understand web technologies for him/her to be able to perform effectively at their job of prettying up web pages? What is the industry trend when it comes to hiring people to improve the look and feel of the website?
However, if your site has complex requirements, needs to work with PHP, ASP, CMS, databases, Ajax or similar, you will definitely need a web developer. While not impossible to find, a designer that also does complex coding (and one that is great at both) is rare.
"Know" is a very ambiguous term.
A good web designer has a grasp of #1. A better designer may grasp #1 and #2. Few web designers may grasp #3.
The level of knowledge required really depends upon the existing construction and desired edits. Remember "web design" is not "web development" in many cases. Although the lines get blurred, web design is the body shop, whereas web development is more the engine mechanic.