Shooting buildings and monuments at twilight works especially well. See how the light changes this image of the Eiffel Tower.
One way to appreciate the power of twilight is to shoot a sequence of pictures from an hour or so before sunset to an hour or so after. This needs a couple of hours of your time, but the results will demonstrate how the sky changes.
Try to find a scene with an interesting subject in the foreground or middle distance. A building, statue or rock formation is ideal. Have your camera on a tripod so that it does not move between shots. However, this is not essential, providing you shoot from about the same position for each exposure.
You need an evening with a fairly cloudless sky. Take the first picture about an hour before sunset, then shoot at 10 or 15 minute intervals. Keep shooting until an hour or so after sunset. When you view the images in sequence you should see the sky change from blue to red to dark blue to black.