Let $S$ be a finitely generated graded $A$ algebra, where $A$ is a commutative ring with unity. The exercise says to describe a natural structure morphism from Proj $S$ to Spec $A$. I would appreciate some assistance! Thanks!
If $B$ is an $A$-algebra, then there is a canonical morphism Spec $B \to$ Spec $A$.
Now if $S$ is a graded $A$-algebra, then Proj $S$ is a union of various Spec $B$'s, as $B$ ranges over certain $A$-algebras, constructed from localizations of $S$. Each Spec $B$ has its canonical morphism to Spec $A$, and these are compatible on overlaps, defining the required morphism Proj $S \to$ Spec $A$.