Pay attention to the spacing of the poem on the page. And the way the lines are broken is a functioning part essential to the poem's life. Therefore, I suggest that, when you read aloud, in addition to giving every mark of punctuation its due, you give space its due as well. Many scholars believe that Dickinson's dashes and spaces are tonal cues. And, surprisingly, with all their idiosyncrasies, Dickinson and cummings use good syntax.
All poems have rhythm.
For a thousand years, English poetry used regular rhythm called meter based upon the regularity of a certain number of normal stresses upon syllables in a line of poetry. No modern poet uses this convention anymore. As far as rhyme is concerned, though no one talks in rhyme, good poets fit the rhymes as well neatly into normative English expression, as the poems here attest. Reading aloud will give you a perception of plot. Every poem has a plot that is, characters, setting, rising action visual to the reader's mind's eye, and climax.