You can't train a Milton. Some people are born great poets and some are not. You can, however, teach almost anyone to appreciate and understand poetry, and by so doing help to broaden their horizons immeasurably.
Poetry analysis should be part of any high school literature course, though introducing it as a subject earlier is a good idea. While poetry remains one of the least read literary genres, it is arguably the most important. It certainly takes the most effort to understand, written as it often is in an obscure and highly metaphorical style. Because of this, a grasp of its essential elements will lead to a level of analytical proficiency students who don't study poetry will likely never attain.
There are a lot of approaches to the study of poetry. Some prefer to learn only the formal elements and to construct a completely objective standard for judging a poem's worth, mostly on a technical level. Others pursue the soul of poetry and dwell on its beauty and spiritual value. Some like to focus on analysis of existing poems, others like to guide students in drafting their own.
The best approach is a balance of these extremes. To understand and fully appreciate good poetry one needs to be familiar with the formal elements, just as one needs to have a handle on poetic diction and metaphor to be affected by the beauty of a well-crafted line. As far as analyzing and writing poetry, for most people the former is enough, though trying to pen some verse of your own is a good way to get a feel for the poetry of others.
Our collection of books on the topic represents all of these approaches. Most provide a more or less balanced course, each with their own strengths. Any introduction that doesn't include at least a passage concerning the beauty of poetry is insufficient. After all, the study of poetry isn't just an academic one—it is ultimately a spiritual and an aesthetic one.