Learn Italian: Mia sorella si laurea in medicina domani. - My sister graduates in medicine tomorrow.

To report this statement in the past, the present tense verb si laurea shifts back to the imperfetto (imperfect) tense, becoming si laureava. You would say, for example, Ha detto che sua sorella si laureava in medicina. Remember that when reporting speech in the past, time words also change, so domani (tomorrow) would become il giorno dopo (the next day).

Why is it Mia sorella and not La mia sorella?

In Italian, you must drop the definite article (like la or il) before possessives when talking about close family members in the singular. So it is always mia sorella (my sister), never la mia sorella. If the family member is plural, you put the article back: le mie sorelle.

Why do we need the word si before laurea?

The Italian verb for 'to graduate' is laurearsi, which is a reflexive verb. Because the subject of the sentence is mia sorella (she), we must use the third-person reflexive pronoun si. The structure literally works a bit like 'she graduates herself'.

Since this happens domani (tomorrow), shouldn't we use the future tense si laureerà?

You absolutely can use the future tense here, but it is not strictly necessary. Just like in English, Italians frequently use the present tense to talk about future events that are already fixed, certain, or scheduled. A graduation happening tomorrow fits this rule perfectly.