Seems very simple. They
just subtract the number of electrons in the Bader region from the number of
protons. Thus, the partial charge on oxygen is 8 - 9.1566 = -1.157, and in
the hydrogen region it's 1 - 0.4238 = +0.576.
Here's the relevant section of the paper:
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Three Bader regions were found, each containing one atom. The total charge in each one of the regions around the hydrogen atoms contained 0.4238 electrons and the oxygen region contained 9.1566 electrons, which gives a sum of 10.0041 electrons. The atomic partial charges are the same as found by Bader [2] (see Table 1), showing that these two different algorithms yield the same results.