This jargon parallels the jargon of cladistics, which is not surprising; a baramin is essentially a kind of clade. As to identifying baramins, many creationists use the Bible; they find out which "kinds" are mentioned in it. But there are numerous species that the Bible says little or nothing about, and many creationists also borrow techniques from mainstream taxonomy -- and also use some rather subjective criteria.
However, creationists have had great differences in opinion as to what baramins there are, and they often describe baramins in very imprecise terms. This may be related to whom their intended audience is, which is mostly people unfamiliar with Linnaean nomenclature, but it is not very helpful to a serious biologist.