There are various ways the appearance of a poem can impact the reading of a work. A good way to view them would to be to put them on a continuum of micro- to macro-focused. A micro aspect would be where the poet decides to end a line. The poet doesn't even need to change the meter of a poem for the poem to be impacted by appearance. Words that start the line, start a verse, end a line, or end a verse naturally have emphasis.
However, this emphasis can be furthered by messing with meter. For instance, a line of iambic pentameter, a form commonly used in Shakespeare's sonnets, has ten syllables. It is common to find Shakespeare messing with his form and having lines with nine or eleven syllables. There is also a term called substitution where a foot of a line is changed in an otherwise normal metrical pattern. An example of this would be a trochaic substitution (a da DUM sound would become a DUM da sound). Another example, not involving meter, would be simply moving from a long line to a short line. An even smaller example would be the length of words and even the length of spaces. With this being stated, it should be noted that the micro and macro explanation is not concrete. If an entire poem was composed of an abnormal amount of large words, it would be noticeable relatively quickly.
Moving toward the macro end of the scale, there are changes in appearance that are apparent for the whole poem. A haiku, a sonnet, or any form has a historical background. Haiku are traditionally about nature, but one can make a haiku about modernization and use the haiku form to make a statement. Another example would be "If We Must Die" by Claude McKay, a prominent African American poet and writer. The poem is done in the sonnet form, and using it, Claude McKay is able to press issues he faced as an African American man in the United States due to the historical background of the form and the literary tension of the time period (the Harlem Renaissance happened during this time).
As for actually vocalizing the appearance of a poem, there is a plethora of techniques. Taking "If We Must Die" as an example, the poem is in iambic meter. It has the rhyme and the flow, but because of the source and meaning behind the poem, I see an indignation that can be voiced when reading it. But there is no strict pattern or rule for poetry in general, and that makes poetry something beautiful.