Illustrator: Isolating and Vectorising a scanned logo

Have you ever found yourself in the situation where you need to take a poor-quality scan of a logo and make it into something scaleable and clean? Sure, you could recreate the logo from the ground up, but that’s time-consuming and labour-intensive. What I’m going to present here is a technique you can use to tidy up a noisy logo and make it into a vector graphic using Adobe Illustrator, quickly and effectively.