Hmmm... interesting question. What "vintage" are you looking for, exactly? There are a few, probably interrelated, questions here:
1. Is it a particular time period?
2. Is it a particular look?
3. Is it a particular photographer?
Sometimes, as Chris mentioned, what makes the photos look the way they do is a combination of technical factors inherent in the equipment itself. Sometimes it's in the subject matter. Take portraiture for an example; not only has the appearance of the photo itself has changed, but types of dress change over time, and the poses used in portraiture of even a relatively recent vintage -- the fifties, for instance -- is different than today, and also different than what preceded it from, say, the 1890's. Photographers working in the same genre have also relied on different forms and techniques over time. Matthew Brady, Robert Capa, and Nick Ut may all have been war photographers, but their approaches to their subject couldn't have been more different.
So what's this mean for you? In short, it comes down to two things: figuring out what you're trying to get across (what's this picture about, and how integral is the vintage appearance to that?); then, paying attention to details. The wrong detail (a vintage diner with a Scion parked out front, someone in Victorian garb doing the Macarena) can wreck the effect even if you've gotten many of the other bits right.