Learn Italian: Non sono mai stato a Roma. - I have never been to Rome.

In Italian, 'never' usually requires a double negative. You put non before the verb and mai after it. Literally, this sentence says 'I am not never been to Rome.'

Where exactly does mai go when using a two-word past tense?

In the 'passato prossimo' past tense, mai goes right between the helper verb (sono) and the past participle (stato). You will do the exact same thing with other adverbs like sempre (always) and già (already).

Isn't stato the past tense of stare (to stay)? Why does it mean 'been' here?

You are right! But in Italian, stato does double duty. It is the past participle for both stare (to stay) and essere (to be). So sono stato is used for both 'I have stayed' and 'I have been'.

Would a woman say this sentence differently?

Yes! Because the helper verb here is essere (to be), the ending of the past participle must match the gender of the speaker. A female speaker would change the 'o' to an 'a' and say: Non sono mai stata a Roma.

Why is it a Roma instead of ?