Okay... There are plenty of Instructables here that explain how to build LED circuits, so we will not be reviewing that except to provide a few links.
My 'ible on Light Pens
covers it as well as this tutorial on my web site.
Also see LEDs-for-Beginners.
And search for LED
to find many others.
Here are 2 recent creations.
The first is a light stick I built for the Maker Faire. It is a great light drawing device that will make a big picture quickly. See our Best of Maker Faire Light Doodles here.
The second uses a geode we found in a rock shop which makes an unusual home display.