Drag and drop should work pretty well, but if you prefer, you can use the buttons on the middle toolbar. You can also use keyboard shortcuts.
For example select an event clip and type E to add it to the end of your project.
More info here. http://help.apple.com/imovie/#mov3a62377a
try known good content. You can download quicktime sample files here:
Try to move one of these into a project. If they were then unfortunately it is your content that is the problem.
open up another user on your mac. Import a clip into iMovie in this user and try to add it into a project.
If it works in a new user iMovie is fine. Your issue can be one of several things. Fully quit iMovie. What I would do is clear all caches found in your ~/library. Move all com.apple.iMovieapp files from ~/library/preferences to your desktop. Launch iMovie and try again.
If it doesn't work in a new user, reinstall iMovie.