I've read a lot of the SCJP questions here, and all the tips and tricks from Sun and the Head First publishers, and I wonder if I am missing something.
I'm having trouble moving from knowledge about a component of Java to being able to answer a question that applies that knowledge. If you asked me a specific question about the language or API, I could answer it. However, when I am looking to apply that knowledge to answer the mock coding questions, it takes me forever to process the question, and I have trouble connecting the dots. It's like nothing clicks. Is there a process by which I can better draw conclusions about questions based upon what I know?
Simple: you use it.
That may sound trite but there is no substitute for learning something new in programming than trying to do something with it. As in writing code.
If it's really new, you might start by taking an existing program and modifying it to do something you want. This will usually break it and you'll spend the next 2 hours working out why. In that 2 hours you'll have learnt more about the basics of program structure (in that language/framework), how a program is put to together and so on than 5 times that long reading it from a book.
Not that I'm suggesting books are worthless: far from it. But programming is ultimately a pragmatic discipline.