Let $X$ and $Y$ be normal toric varieties whose underlying lattices are $N_X$ and $N_Y$ respectively. A toric map is a morphism $f : X \to Y$ that induces a morphism of algebraic groups $g : T_X \to T_Y$ such that $f$ is $T_X$-equivariant with respect to the $T_X$-action on $Y$ induced by $g$. Every toric map $f : X \to Y$ corresponds to a unique map $f_N : N_X \to N_Y$ between the underlying lattices such that, for every cone $\sigma$ in the fan of $X$, there is a cone in the fan of $Y$ that contains the image $f_N(\sigma)$. For details see Theorem 3.3.4 in Cox-Little-Schenck.
To specify a map of normal toric varieties, the target and source normal toric varieties need to be specificied as well as a matrix which maps from $N_X$ to $N_Y$.
The primary constructor of a toric map is map(NormalToricVariety,NormalToricVariety,Matrix).