Learn Italian: Mangiamo una pizza in pizzeria stasera. - We are eating a pizza at the pizzeria tonight.

You would use the "we" form of volere, which is vogliamo (we want), and change the main verb back to its dictionary form (the infinitive). The sentence would become: Vogliamo mangiare una pizza in pizzeria stasera.

The English translation says 'We are eating', but doesn't mangiamo just mean 'we eat'?

In Italian, the simple present tense covers both! Mangiamo can mean "we eat" (as a general habit), "we are eating" (happening right now), or even "we are going to eat" (as a plan for tonight).

Why is it in pizzeria instead of using a or alla?

In Italian, types of shops and businesses that end in -ia (like pizzeria, gelateria, or farmacia) almost always take the preposition in, usually without any article like "the" or "a".

Is the word stasera related to sera (evening)?

Yes! It is actually a mash-up of questa sera (this evening). Italians drop the first part of questa to make the shorter, everyday word stasera (tonight). You will also see this pattern in stamattina (this morning).