Goleman's the guy who came up with the term emotional intelligence. His book on the subject is really interesting, although I haven't read any of his other work (and yeah, I'd be a bit skittish of that spirituality book as well). As to your question, Goleman talks about there being nine different kinds of intelligence in the book. I'm not sure how much actual evidence there is for its existence, but I will say that a. we're still at a pretty early stage in understanding the workings of the mind, and b. I think there's still some utility in considering it even if it turns out to not be entirely true.
As for how to gain skill in it... it's probably one of the more, if not the most intuitive-mind sided intelligences Goleman proposes. There might be books on the subject which would help if you're *really* clueless as to what various facial expressions/other body languages mean. Beyond that, hanging out with other people a lot is probably going to be the best/only way to really gain expertise in the subject (and on a side note, consider how much some people hang out in groups like that, unconsciously practicing their trade. One of the better takeaways from Goleman's book is the understanding that "social butterflies" aren't necessary dumb just because their area of study is in emotional intelligence and social interaction as opposed to logic or reading comprehension).