Rule 1. First of all, use the ever suffix when who or whom can fit into two clauses in the sentence.

Example Give it to whoever/whomever asks for it first.
Give it to him. He asks for it first.

Rule 2. Because we can substitute him and he into both clauses, we must use the ever suffix. Now, to determine whether to use whoever or whomever, here is the rule:

him + he = whoever
him + him = whomever

Therefore, Give it to whoever asks for it first.

Example We will hire whoever/whomever you recommend.
We will hire him. You recommend him.
him + him = whomever

Example We will hire whoever/whomever is most qualified.
We will hire him. He is most qualified.
him + he = whoever