When I was in tenth grade, my English teacher spent about one half of the year on "poetry appreciation". If this had been my only experience with poetry, I am certain I would despise poetry. We were required to count the meter of the poetry and listen to our teacher's explanation of what the poem meant. We were not allowed to disagree with her explanation. Tests were given as essays in which we were expected to parrot back her explanation of the poems.
I objected to this analytical way to appreciate poetry. I loved poetry, and had dabbled in writing my own verse. I tended to read poems for the feel of them, allowing the pictures they painted to form in my mind. Unsurprisingly, there came a day when I disagreed with this teacher's explanation of a particular poem. I wanted to know if I was allowed to put my own interpretation of the poem on the test, should the poem be covered on the next exam. She accused me of cheating, because I must have seen the test. The test day came, and this poem was on the test. I wrote down my own interpretation of the poem, with supporting information. I failed that question.
I don't write this to put down English teachers. I had just the one bad English teacher experience. I am using this to illustrate how many people might think they don't enjoy poetry because of a similar negative experience. After an experience like this, poetry may never be approached again. But you probably have more experience with poetry that you like than you realize. Most songs are poems, and a good one will stick in your head for days.
Some good beginning poetry books include any of Shel Silverstein's poetry, A Child's Garden of Verses (not just for children), The 100 Best Poems of All Time, and Best Tales of the Yukon.
Here is another poem I have enjoyed by Emily Dickinson:
There is no frigate like a book
To take us lands away,
Nor any coursers like a page
Of prancing poetry
This traverse may the poorest take
Without oppress of toll;
How frugal is the chariot
That bears a human soul!