Learn Spanish (Latin America): Al partir, ella miró la casa. - Upon leaving, she looked at the house.

You are right that al is usually the contraction of a plus el meaning 'to the'. However, when you put al right before an infinitive verb like partir, it acts as a grammatical shortcut to create a time-related clause meaning 'upon doing something' or 'when doing something'.

How do we know the leaving happened in the past if partir is in the infinitive?

The al plus infinitive structure never shows the tense itself. Instead, it borrows the time frame from the main verb in the sentence. Because the main verb miró (she looked) is in the past tense, we know the leaving also happened in the past.

What is the difference between using partir here instead of salir?

You could easily use al salir or al irse here. The verb partir means 'to depart' or 'to set off' and sounds just a bit more formal, dramatic, or literary than the more everyday verbs salir (to leave) and irse (to go away).

Do I have to include the pronoun ella here?