Writers love quotes because they add human interest and immediacy, but most people you want to quote don’t talk clearly. You have several options: don’t quote them, paraphrase, use a partial quote, ask the question again or sharpen the answer.
You use a quote because it’s the best way to explain something or to capture character. But quotes require a lot of apparatus (attribution, identifying speakers and context), so you should use them sparingly. Don’t quote just to quote. And apply even more rigor to poorly-phrased quotes. So first, just leave them out.
You can always paraphrase a quote. If you can write it better than the source said it, you probably should. Some paraphrases include short bits of quoted material, what we call a “partial” or “fragmentary” quote. Read more