Dick Costolo, the chief executive of Twitter, has tapped his background as a former professional comedian to run what has become one of the most important companies in Silicon Valley, according to a long profile in the New York Times.

San Francisco-based Twitter is often mentioned as the next major initial public offering candidate in the social media space. But that’s only going to happen if Costolo guides the firm in the right way. (Some critics think a Twitter IPO is very unlikely, after Facebook’s weak performance. Twitter’s revenues for 2012 are expected to be about $350 million this year.

And Costolo isn’t just winging it. He’s embracing improvisation and is communicating both inside and outside in a way that taps his stand-up comedian skills. Costolo can stand up in front of all of the employees and “just work the crowd,” the Times quoted one employee as saying. One way that Costolo has become more comfortable as CEO is that he says he doesn’t mind so much that he’s older and bald, in contrast to the spate of social media startup CEOs who are young and svelte. He thought about his “un-CEO demeanor,” he says, and concluded that he doesn’t care. The story doesn’t dwell that much on Costolo’s decision to oust some third-party applications from Twitter, a move that angered developer partners.

One of the interesting parts of the story is the reason for the reduced role of Jack Dorsey, co-founder of Twitter. Dorsey left to found Square and came back to help Twitter. But the Times quotes one person as saying that Dorsey didn’t get along with the employees so well and that he isn’t decisive. Costolo, on the other hand, is decisive. And he’s ad-libbing.