I slip in the passato remoto (simple past tense), like l'altro giorno andai al mercato (the other day I went to the market), every now and again in my conversations these days. I read the passato remoto quite often as it is frequently used in books. My friends here in Florence use it quite a bit even for events that have just happened; however, my other Italian friends rarely use it at all. For them, the passato remoto is to be used with events much farther in the past, not things that happened yesterday.
I used to shy away from using the passato remoto because it sounds so different from the normal passato prossimo (present perfect tense), like sono andata al mercato oggi (I went to the market today), and also it doesn't follow the standard verb ending rules. Normally, all verbs in the first person end with "o," but not in the passato remoto where they usually end in "i."
Not only that, but sometimes the verb looks nothing like the infinitive verb. For example, seppi (I knew) is from the verb sapere (to know) and fu (he/she/it was) is from the verb essere (to be).
Some people will argue that the Florentines misuse the verb tense, but it is what is used here. You don't have to use the passato remoto, but it is used quite a bit so it's a verb tense you have to understand.
The actual rule is that the passato remoto should be used to define events in the past (like in history) or an event that has passed and is no longer completed.
For example, I use it to say, "Mio nonno nacque in Italia." (My grandfather was born in Italy). I can't say "é nato" because he is now deceased, so the proper way to say that he was born somewhere and that he is also no longer living would be to use the passato remoto.
I love the Italian language for its richness and complexity even though there were times I banged my head against a wall when I was learning it.
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