Nothing trumps a concrete example
When trying to convince someone that you have a learning example in a very short amount of time, it is an good option that you give them a concrete example of how you tackled the knowledge in an unfamiliar field. The following shows the example I would provide if I am being interviewed for a job that requires a good learning attitude.
The learning attitude of me
In my case, if I am faced with a totally new area, Wikipedia would be a very good start for me. I would learn the key concepts in that area from Wikipedia and probably some external links. This is step one, and I call it "defining the area".
Next, I would start with books on that particular subject. You don't want to spend your precious time reading through a thick book that is poorly written. So, I would ask Amazon.com for help. There are many good people who share their reviews on books about your targeting subject. I would go through the review of those books. Note that, we should read both the five-star reviews as well as the one-star reviews, since sometimes the reviewers who give only one star have their unique insights on the drawbacks of that book. This is step two.
After I find the right book, things become easy and hard. It's easy because you now know what to spend time on -- the book. However, following a book carefully can be hard and boring, and it takes time. I'll try to be patient, because I know that the seemingly hard way may also be the easy way, since reading through a book requires minimum amount of dependencies from outside of the book.
Once I've gained the basics, I would do some real projects in order to polish my skills. Then, online forums and Google kick in. The process of polishing one's skills can be unbounded in terms of time. Just spend time at it, and you will improve gradually.
Time and experiences matter
Learning attitude is not like a recipe that once you get, you get it all. It's a ongoing process of gradual improvements. Improve by actually doing it.