I'm reading section 6.3 of Vakil FOAG. In it he defines a morphism of $k$-schemes $X,Y$ as a morphism of schemes that commutes with the maps $X\longrightarrow \operatorname{Spec} k$ and $Y\longrightarrow \operatorname{Spec} k$.
I'm struggling with this concept in practice; for example, how does one find all the morphisms of $k$-schemes between $\mathbb{P}_k^1$ and $\mathbb{P}_k^1$?
We want to form a commutative diagram with morphisms going to $\operatorname{Spec} k$, which is $0$. So I feel like this should be easy, but how to proceed?