It's always interesting to me to hear how writers view the act of writing. Given we all spend much more time than any sane person ever would, thinking up similes and metaphors, we tend to anthropomorphize or animate just about everything, including whatever it is that empowers, enables, forces, etc. us to write.
Traditionally muses were women, often young and beautiful, which makes sense given the derivation of the word. Stephen King described his muse as a guy who sits in an armchair smoking cigars. The more regular Mr. King was in his writing schedule, the more likely his muse would show up and keep him company.
For me each story has its own kind of muse, and they're all wild, mythical, never before seen animals. For me, the challenge is harnessing them without killing them. If I'm too heavy handed, they become too tame and the resulting story might have some technical merit, but that's about it. So when I'm writing, I go through phases. In the early phases, I try to find the form and shape of the muse. For that I write a TON of verbiage that I will later throw away. Only when I feel confident that I know what kind of beast this is do I move in aggressively. The ideal result for me is to have the muse all hitched up to drive the story, without it being so tied up that it can't take off running and pull the reader through the pages.
What's your muse look like?