The number of guns in the hands of the American citizens is often reported to be anywhere from 270 million to 300 million. I was curious and was going to start digging round a little bit, and then I saw in one of David Codrea's articles.
November 14, 2012 Congressional Research Service report on “Gun Control Legislation” (pdf)
From that report:
2009, the estimated total number of firearms available to civilians in the United States had increased to approximately 310 million: 114 million handguns, 110 million rifles, and 86 million shotguns.
That's a good place to start counting the number of firearms available to the American people.