有一天: past as well as future? I'm told that to express something as "one day" in the future, it's 「有一天」. For example, 「我希望有一天能够说好华语。」"I hope that one day I can speak Chinese well."

Would you also use this to the English idiom "one day" in the past, such as "One day, the boy went for a walk"? Would that be something like 「有一天，这个男孩儿出去走了走。」?

Pardon the bad grammar.
Yes, `one day' can certainly be used to refer to events in the past as well. 

A better translation of "One day, the boy went for a walk" could be "有一天, 那个男孩外出散步", or less literary, "那个男孩出门走路". "去了走路" is not grammatical, "去走路了" and "走路去了" are grammatical but do not fit in here.