Learn Italian: Mia madre sta stirando una camicia.

In Italian, the present progressive tense (doing something right now) is formed using the verb stare (to stay/be), not essere (to be). Since "my mother" is the third person singular ("she"), we use sta.

How do we form the word stirando?

Stirando means "ironing". It comes from the verb stirare (to iron). To make the "-ing" form (called the gerund) for verbs that end in -are, you drop the -are and add -ando.

Could I just say Mia madre stira una camicia instead?

Yes! In Italian, the simple present (stira) can mean both "irons" and "is ironing". However, using the present progressive (sta stirando) strongly emphasizes that she is in the middle of doing it right at this exact moment.

Why isn't there a la before mia madre? I thought possessives usually need an article.

You are right that possessives usually take an article (like la mia macchina for "my car"). However, there is a special rule for family members: singular, unmodified family members (like madre, padre, fratello) drop the article. So it is just mia madre.