A 10 percent change in the county-level circulation of Oprah Magazine is associated with an increased vote share for Obama of approximately 0.2 percentage points. This estimated effect was higher in areas holding caucuses rather than primary elections. In terms of voter participation, a 10 percent change in circulation is associated with a 0.06 percentage point increase in turnout. Similar effects from the endorsement were found in areas with differentially high sales of books included in Oprah's Book Club. In total, we estimate that the endorsement was responsible for 1,015,559 votes for Obama.Roughly speaking, their methodology was to take a county-by-county look at (a) the circulation of Oprah magazine and (b) sales of books recommended by Oprah's Book Club. This is a measure of how many Oprah fans there are in each county. Then they controlled for all the usual electoral variables (age, income, marital status, etc., and especially gender and race since they were unusually important in the 2008 primary). Then they accounted for the fact that Oprah readers are more educated and wealthy than the general public, and the readership is disproportionately African-American. Then they applied their model to Obama's 2004 senate race to make sure that it was really Oprah's endorsement that made the difference, not merely some other variable associated with Oprah fans that they neglected to account for. Finally, they took a look at contributions to the Obama campaign both before and after Oprah's endorsement to control for "potential unobserved county-level preferences for Obama."
This is, as usual, very complex, and there's no guarantee that the authors thought of everything. Still, they've accounted for an awful lot, and they still came up with an extra million votes for Obama thanks to the Oprah effect. Pretty impressive.