Have the start-up write down all the attributes they want their product to have. If you were selling magnificent trained wolves, for instance, you would want the customer to think, upon seeing the wolves: "What proud, mysterious, noble, cunning, ruthless, snow-dappled, and primeval creatures." You would neither want nor expect the customer to generate such adjectives if you were selling, for instance, hamsters.
At that juncture I would repair to a high mountain top, away from the start-up client, one hand lazily petting the head of my fearsome trained wolf, as I mused to myself on the adjectives I had just collected. What colors would they inspire? What noises, what textures, what tastes? I would write all these down in a second list.
Then I would descend back to the company of my human friends and ask people not in the start-up what the second list made them think of, as a cross-check against the first. If you start off with "petwolfco: proud, mysterious, ruthless, loyal", and come back from the mountain with "petwolfco: confetti colors, Comic Sans, merry polka music, Shirley Temples", you had better go back to the top of the mountain to reflect some more.
When my impulses and my third party's impulses at last concurred ("petwolfco: grey, ragged, minimalistic, narrow sans-serif, stunning small highlights in stunning blood red"), I would craft my new logo, working all through the night into the early dawn. As the sun rose pink and gold over the sleeping world, I would deliver that logo into the hands of my start-up client in the form of an extremely high resolution image they could shrink down later if needed. The start-up would gasp in marveling wonder, and clutch the SVG file gratefully to its chest. My pet wolf would nod gravely, and we would stalk wordlessly back into the mountains.
