You can use the passé simple in any formal piece of writing, but as it is quite a literary way of writing, it's generally more appropriate to pieces of writing in which you might be narrating a story. It is used exactly where you would otherwise use the passé composé (focus on the completion of action) and does not replace the imperfect tense. In any piece of writing, whether you choose to use the passé simple or the passé composé, you do have to remain consistent throughout, as they are considered equivalent in terms of meaning, and only different in terms of tone/register.
In general, you would only use it orally in highly formal situations, and even then, it's quite rare nowadays!