Let's be clear from the start. This entry is not about 'sound poetry,' the use of sound as opposed to words as a means of poetic expression. Here we are dealing with the sounds that are language, that form the words we use, and especially of those sounds as they take part in our poetry.
Two incidents brought this to mind recently. First I had taken my cat to the veterinarian for his annual checkup and necessary booster shots. When we got home he was quite put out and avoided me. Some time later I lay down on the bed and invited him to join me. He did, and after some time ended up lying against my chest, purring. In return, I hummed deep in my throat and chest in response. We quietly lay, side by side, exchanging vibrations. It reminded me of how a mother will use a wordless hum to soothe a fussy baby.
Now for the second influence. I was reading a passage of poetry aloud to myself when I noticed that the author had used an unusual number of 'm' and 'n' sounds in one of the four line stanzas, and the soothing effect (much like the cat or a baby) that had on me. I had read the poem before, but never aloud. I was so intrigued that I read the poem again several times, this time emphasizing and lengthening those sounds. Granted, I sounded as if I suffered from an acute stammer, but it certainly heightened the effect.
I thought about how poets when they read their work aloud in public seem to ignore the importance of sound in favour of putting across the meaning of the words. Seldom is there any lingering over a single sound or emphasis on a series of sounds. And sound is so important to poetry. We use its repetitions to enhance our words: rhyme, both at the ends of lines and internally, and with its many elaborations; alliteration, the repetition of initial consonants; assonance, where the vowel sounds repeat but not the consonants; consonance, where the final consonants agree in sound but the vowels do not. And, of course, the many variations of these.
So if a poet goes to all that trouble to use it in the written word, why not note it in the spoken? It doesn't take much. It is not necessary to stop so long that the silence underscores it, or to voice it in such a way as to bring undue attention. The simple answer is to read slower. If we read slower than normal speech (and speech in modern times has tended to quicken noticeably), the hearing ear can catch patterns of sound that could easily pass ignored. Those patterns of sound are as much of the poem as the words and meaning.
So, poets at the mike. Slow down the tumble of words; sing out the sounds.