Learn Italian: I miei genitori si sono sposati a Milano.

In Italian, all reflexive verbs (like sposarsi, to get married) must use the helping verb essere (to be) in the past tense. Because of this rule, you use sono instead of hanno.

Why does sposati end in -i here?

Because reflexive verbs use essere as their helping verb, the past participle (the main action word, sposato) has to agree with the subject. Since I miei genitori (my parents) is masculine plural, sposato changes to sposati.

Where does the reflexive pronoun si go in a past tense sentence?

The reflexive pronoun (si) always goes immediately before the helping verb. That is why it is si sono sposati, and never sono si sposati.

I thought we drop the article for family members. Why is it i miei genitori instead of just miei genitori?

You drop the article only for singular family members (like mio padre, my father). When talking about plural family members (like parents, brothers, or sisters), you always bring the article back. That is why you need the i here.