The Electronic Frontier Foundation's Mark Rumold has detailed analysis of yesterday's story about the bizarre, misleading way that the NSA uses the word "targeted" in discussions of "targeted surveillance." It comes down to this: the NSA and its defenders continue to claim that the organization only spies on foreigners when they're off US soil, and not on Americans or people in America (why this should comfort those of us who are neither Americans nor in America is a mystery to me).
But they harvest every word read and written on the Internet, including private communications, and scan it to see if it matches the name of someone they're looking at — say, Vladimir Putin. Anyone whose communications contain the name or other details of the foreign target can also be spied upon, and the NSA says this doesn't constitute domestic spying. So they're not spying on all Americans, just every American who's ever mentioned the name of a foreigner — and to accomplish this, they read every word everyone writes, but they're using a computer to do it, so it doesn't count.
First, at least this much is clear: a "target" under the FAA must be (a) a non-US person and (b) not physically located within the United States. A "person," for purposes of the FAA, includes individuals as well as "any group, entity, association, corporation, or foreign power." Under the FAA, the government can thus "target" a single individual (e.g., Vladimir Putin), a small group of people (e.g., Pussy Riot), or a formal corporation or entity (e.g., Gazprom).
So, when the NSA decides to "target" someone (or something), it turns its specific surveillance vacuum at them. The NSA then believes it can intercept and analyze all electronic communications of the target (telephone conversations, email conversations, chat, web browsing, etc) so long as the "target" is overseas and remains overseas. As others have noted, this includes conversations the "target" has with Americans, which would then be "incidentally" collected. Keep in mind this does not require a warrant or even the approval of a court, which is only one way Senator Feinstein's reassurance was demonstrably false. But there's still more.
(Image: Συνάντηση με Πρωθυπουργό της Ρωσικής Ομοσπονδίας, Vladimir Putin, a Creative Commons Attribution Share-Alike (2.0) image from primeministergr's photostream)