I have seen in a paper that the author states that the coefficient he gets in a regression implies that an increase of one standard deviation in the explanatory variable increases the dependent variable in 0.6%

How does the coefficient imply that? How did the author calculate that?

The thing is that now I am trying to write a report and want to make a similar statement, but I do not know how to calculate the change in the dependent variable when the explanatory variable changes in one standard deviation. I tried adding one stdev to all observations, but holding everything else constant, the coefficient did not change. What do I do?

I'll really appreciate any help I can get here.