Sorry I haven't been around deviantart for so long! I'll put an demo on my agenda, in the mean-time, let me try to explain better:
In the study phase you are trying to learn a principle/technique/skill, in the application phase you are trying to use, apply and play with the skill.
Let's say you are studying composition. For the study phase, you would find a illustration by an illustrator you like, that has really good composition. You make a copy of the work and take notes of what they are doing to make the composition awesome. Sometimes this will take some digging, sometimes you may have to read a book or blog post on composition to understand some of the principles, but most of the time yo u should be able to figure some things out on your own, just by making a copy of the piece and thinking hard about it.
Once you think you've identified some principles from your study, start your own illustration and try and use some of the principles you've just learned to make your won piece of art. Play around with the principles, how can you use them differently or vary them from the artist you've studied? If you make a discovery in your own work, take notes on that too! I keep a document where I just write down notes of techniques or approaches I discover.
Does that make sense?