That's a good question. I'd say to start with a solid textbook on psychological (and/or educational) tests and measures. Kaplan & Sacuzzo, Robert Gregory, or Cohen & Swerdlik are all widely used in tests & measures classes. Each will contain 2-3 chapters reviewing the underlying statistics, then covering reliability & validity issues.
However, I've noticed that these textbooks (unlike statistics texts) rarely provide step-by-step descriptions of how to implement the equations they present. So you need to be able to figure that out for yourself. Or, of course, use a statistical software package that contains the necessary functions. Most do, of course. But it is a gap in the literature.
There are books that delve into the statistics on a much deeper level, all the way back to Nunnally's classic text. But they tend to assume that you know how to follow advanced mathematical arguments, something most of us poor psychologists aren't very good at. There is also a "psychometric tests for dummies" book, but I haven't actually seen it so can't say whether it's good or not.
Dissertation research? I remember having to self-teach a lot of this stuff, too...