From Algebra by Hungerford:
Let $R$ and $S$ be rings and $\phi: R \rightarrow S$ a ring homomorphism. Then every $S$-module $A$ can be made into an $R$-module by defining $rx$ $(x \in A)$ to be $\phi(r)x$. One says that the $R$-module structure of $A$ is gen. by pullback along $\phi$.
I find this a bit confusing, because $\phi(r) \in S$ and not in $R$. Then how do we get an $R$-module if the scalars are from $S$?