In trying to describe Always Outnumbered, Never Outgunned to friends, I've sometimes fallen back on the old "X plus Y" trick so common to those pitching a project to a prospective reader, producer, editor, or other authority. In my case, I cited three major sources of inspiration for the project: Martin Scorsese's GoodFellas, James Cameron/Kathryn Bigelow's Strange Days, and Alejandro Jodorowsky's The Holy Mountain. No, really.
This in turn provoked another discussion: what I mean when I say something took inspiration from something else, as I've developed my own take on it over time.
At the start of most any creative career, people imitate. It's a necessary stage in creative development; you have to see what it's like to do something, and one of the most direct ways to do that is to copy someone else's work. One common exercise in creative writing class in high school was to write a story in the manner of Hemingway, in big part because his style lent itself to being so readily copied. Less easy to copy was his state of mind, because that was the single biggest reason he wrote the way he did — and let's face it, it wasn't something anyone would have really wanted to emulate, but it was his.
That's the part I find myself most thinking about when it comes to taking inspiration from something else. Not aping what it does, but trying to dig into the worldview that informed it, and learning from that. When I first started reading Phil Dick and Stanisław Lem and Yukio Mishima, I tried to create things that were informed by what I believed to be the same worldviews. I ended up learning a lot from all three; in Mishima's case, I learned mostly what not to do, because I ended up getting disgusted with most of his work and ultimately repudiating it.
Other peoples' works teach me new ways to look at things. They aren't just repositories for individual story elements. In fact, lifting elements from other stories always seems like the least effective way to populate another story, because you're getting things second-hand that way. Go to what the story points at — the real world things it draws from —and pick up the thread there yourself. I don't think I've seen much instruction for creative types in how to do this.