One of the best pieces of advice I've received as an author is how to write believable dialogue.
When I lived in Virginia, there was a fabulous grocery chain called "Ukrops" that had cafes that were quite popular - either as a coffee shop or for a full meal or anything in between. The advice I received was to get a cup of coffee, sit in the Ukrops cafe and simply listen.
I chose to go there at lunchtime, when many of the government employees who worked at the police department or court house (just a few blocks away) would converge on Ukrops. I'd get my lunch, select a spot near the middle, and listen to snippets of conversation.
From those experiences, I learned how to write what I heard: the inflections, the accents, and the use of informal language. In my earliest books, I read the dialogue out loud and often changed the structure of the sentences to make them more believable. As I continued to write (my 15th book will be released in 2013) developing dialogue became second nature and I rarely need to read it out loud now.
It is also important not to have each character speak exactly the same. It is important that the reader can identify a character by their speech pattern, especially when moving back and forth in a rapid-fire conversation.