This is as big a topic, as you could have possibly opened. Design is controversial, and is generally dependent on the particular individual, or group with common interests.
One of the modern notions in information presentation over the web is flat illustrated parallax design.
http://www.dangersoffracking.com/ is a great example of this method. It uses simple, but beautifully stylized images, and takes the reader on a journey by simply making him scroll.
This of course is something you can only do for presenting informational content.
The main rule about design is "Design follows function". Which means you must first create the architecture of your website, be it informational, commercial, gallery, 2.0, or whatever, first you need to get a grasp of what it will do.
Then tackle the easiest and simple way to do it. When you get it, form this into a page layout, and you've got a website.
Design is far above graphics and colours. It's about usibility. Check out this for UI examples, do's and don'ts. ->
https://www.goodui.org/