only time and frustration. I've just seen many people spend more time with grammar than vocabulary.

as a side note, one annoying thing is that the name of the "cases" (and even the word itself) in English seem like a random collection of letters. Take genitive for instance -- what does this mean?? At least in Russian родительный gives some indication of what this "case" is about (well, if you've learned the root word of the name of this case).

By the way, I still think one of the most effective ways of understand this stuff is to understand the grammar of your native language as well.