I've studied design patterns several times. I read the book, studied with coworkers, and even attended a study session. I think each time I learned more and more depth to the patterns. I think design patterns are something you can revisit many times over and learn new insights and connections between the patterns. Once you start to see similarities in structure between the patterns (say the similar structure between state and strategy pattern or the difference between decorator and strategy) you'll have reached a new level in understanding them.
If people still want to learn more about them. I'd start again and look for opportunities to do coding exercises around them. Or compare and contrast two patterns. Try solving a common problem using two different patterns (strategy, decorator, and template method are good ones to do this type of exercise with). Look for examples in Frameworks that use patterns (What pattern is java.io.InputStream/OutputStream? How about javax.swing.Border what pattern is that?) Or look at other languages and how patterns might be implemented in them (Ruby's .each or .inject method is what pattern?) Then try and explain why the author used that pattern instead of something else.
I also over used them and royally screwed up some software using them. You are going to go too far with them. Abuse patterns and you can easily undo a lot of readability. I think its unavoidable and part of the learning process with patterns. As most developers get so enthralled with the flexibility they give adding unneeded flexibility is too tempting for most. That's not to say design patterns are pointless or without merit, but I think I learned the most about them when I backed away from using them for everything. I still use patterns, but with more wisdom. Refactoring to patterns is typically the best choice.
Which is another avenue you could look into. Martin Fowler's book on Refactoring applies design patterns to simplify and make code more extensible. You could introduce refactoring techniques while also learning how to best patterns.