You know, I learned most of the important stuff in the java library from the javadocs. They are amazingly easy to navigate, and it's a really good idea to get in the habit of referencing them.
Just start here:
http://java.sun.com/javase/6/docs/api/
in the right-hand frame. It has a bunch of packages. Review each one and look at the package summary. This will get you the knowledge of what's available and about where to find it.
When you encounter an interesting package--click on it and explore. The package summary generally has a really good readable description of exactly what the classes does complete with class breakdowns, links to tutorials--I'm surprised they don't have circles and arrows and a paragraph on the back of each one explaining what each one was to be used as evidence against us...
When you are coding, keep the screen up. You can search for any class by name, the classes are all listed in the lower-left panel.
Finally if you "Kindof" know what method you want, there is an "Index" link at the top that will show you all the methods by name (Only works if you know the first letter). Once located, you can figure out the classes that implement that method.