We say Auguri! when it's the new year or when someone has a birthday. Tanti auguri a te is how Italians sing, "Happy Birthday to you." But we also have the verb augurare, which is used quite frequently, even on ordinary days.
Non le posso augurare una buona sera perché non è una buona sera.
I can't wish you a good evening, because it isn't a good evening.
Caption 21, La Tempesta film - Part 22Play Caption
When you wish for something, you hope it will come true. In English, we either use the imperative of the verb "to have," or we can change the construction and use the verb "to hope."
Ti auguro una buona giornata (have a good day/I hope you have a good day).
If you follow Marika's videos, she almost always wishes you a marvelous day at the end.
Io ti auguro una giornata meravigliosa e ci vediamo la prossima volta.
Have a marvelous day and I'll see you next time.
Captions 56-57, Marika commenta -La Ladra Espressioni idiomatiche - Part 1Play Caption
We can use augurare with a reflexive ending, too: augurarsi. We use this form when we want to say, "I hope so!" We say:
Me lo auguro (I hope so).
Mi auguro di sì (I hope so).
No, scusi, mi auguro che Lei abbia una motivazione plausibile, perché se no io... -Ma un istruttore a che Le serve?
No, excuse me. I hope you have a plausible reason, otherwise, I... -But what do you need an instructor for?
Captions 9-10, Il Commissario Manara S2EP7 - Alta società - Part 13
Note that after mi auguro comes che, and some of us know what that can mean. It likely means we'll need the subjunctive. In the example above, we do indeed need the subjunctive of the verb avere (to have). For more about cases like this one, see our lessons on this topic.
Using me lo auguro can have a somewhat negative nuance and we might translate it as, "I should hope so!" So it's not really hope, but rather expecting something to be a certain way. It's also quite a mouthful of vowels. Luckily, you can also say:
Lo spero (I hope so)!
On the other hand, if we want to say "I hope not," we can simply say mi auguro di no.
Hai imparato qualcosa (did you learn something)? Mi auguro di sì (I hope so).