Nihilism (or at least my version of it) does not say that one should "do nothing", but instead that there are no values (i.e., one is indifferent between all possible states of the world). If one does consider all possible states of the world to be equally preferable, there is an additional complication that our minds are largely collections of autonomous processes that are not affected by consciously held values, so you do not end up doing nothing even if you do end up being a nihilist. Instead, the part of your mind that is motivated by explicit verbal/philosophical considerations is no longer motivated to do anything, and leaves the rest of your mind to run your body on automatic. (If nihilism does say that one should do nothing, then you'd actively try to stop yourself from doing anything, but that's not my claim.)