Page 11 of Fulton's "Toric Varieties" gives the following procedure for finding generators of the dual of a convex polyhedral cone in $\mathbb{R}^d$:
For each set of $n-1$ independent vectors among the generators of $\sigma,$ solve for a vector $u$ annihilating the set; if neither $u$ or $-u$ is nonnegative on all generators of $\sigma$ it is discarded; otherwise either $u$ or $-u$ is taken as a generator for $\sigma^{\vee}.$
What does it mean to annihilate the set? I suspect it means that $\langle u, \cdot \rangle$ vanishes on the set, but then $u=0$ trivially always works. Should he have said $u$ must be non-zero? He never said what $n$ is, I guessed it is the number of generators of $\sigma.$ But then, if we found a $u$ that annihilates $n-1$ of the $n$ generators, then one of $u$ or $-u$ is certainly nonnegative on all generators, so we would never throw any of these $u$ away. Can someone clarify what the correct steps are?