何と言ったら良いか分かりません means "I don't know what I should say."
But what is the literal translation of this sentence? What is the purpose of the
you can think of it like:
What to say... / good? / I don't know
the か would supply the question mark in my literal translation above.
か indicates a question. In English, questions in the main clause will be indicated by inverting the auxiliary before the clause. The addition of か in Japanese corresponds to that, but in Japanese, か is added regardless of main or embedded clause.