Being hungry in Italian is quite different from being hungry in English.
It's not just that Italians are more passionate about their food. It's not just that being hungry is a catastrophic event that must be immediately remedied with a quattro formaggi pizza.
The difference is that in Italian, instead of being hungry, you have hunger.
So here's a good opportunity to learn the very useful auxiliary verb, avere — "To have".
Let's see it in action by talking about how hungry we are!
In Italian you can actually leave out the personal pronoun in front, unless you really want it for emphasis or clarity. There's enough information in the verb for Italians to figure out who you're talking about.
There are many other instances where Italian speakers "have", instead of "be". For instance, you can also have thirst, sleepiness, hotness and coldness.