Well, we (or I at least) read a lot of class defenitions. I'm not really familiar with all of UnrealT's classes. Usually when I want to create something, or answer someone's question, I look through all the parent classes of the class I/someone are/is trying to create and see what functionality is provided, and change or build on that.
A tip: Use Windows/UClasses search "containing" functions a lot. It's really good to find out where a function is called, or where it is defined, which is a good way to get familiar with the classes. Stuff like the fact that "Modifyplayer" is called in the GameInfo class are handy to know.
As for that Syntax and problem solving, it's really a lot like C, and I was familiar with it before I started UScripting.