Two statements are equivalent if... Two statements "If A, then B." and "If P, then R." are equivalent if the validity of one statement implies the validity of the other?
That is, I assume that "If A, then B." is valid, then proceed to show the second statement is valid, and vice versa?
Or this done differently?
To show that a statement is valid, one need only show that if the premise is true, the conclusion necessarily follows, right?

Material equivalence between statements $p$ and $q$, denoted by  $p \leftrightarrow q$, is logically equivlaent to $(p \rightarrow q) \wedge (q \rightarrow p)$. 
Hence, if you wish to show that statements $a \rightarrow b$ and $p \rightarrow r$ are equivalent, or $(a \rightarrow b) \leftrightarrow (p \rightarrow r)$, then you may do this via natural deduction if you can show $[(a \rightarrow b) \rightarrow (p \rightarrow r)] \wedge [(p \rightarrow r) \rightarrow (a \rightarrow b)]$.
A general strategy to do this, known as a direct proof, would involve exactly what you are saying. First, assume $a \rightarrow b$ and then validly deduce $p \rightarrow r$. Secondly, assume $p \rightarrow r$ and then validly deduce $a \rightarrow b$. If you can do both, then you have demonstrated equivalence.
