Vorrei means "I would like" and is the polite way to order: just put a noun after it (Vorrei un caffè) or another verb in its basic -are/-ere/-ire form (Vorrei pagare). Use the indefinite article un (masculine) or una (feminine) with the thing you want.
Examples
- Vorrei un caffè e una brioche, per favore.
- I'd like a coffee and a pastry, please.
- Vorrei vedere il menù.
- I'd like to see the menu.
- Vorrei pagare, il conto per favore.
- I'd like to pay, the bill please.
The mistake to avoid
"Voglio un caffè" is grammatical but blunt — in a café use vorrei.
Where this fits in
Food & ordering, Italian A1: Order at a café or restaurant, ask for the bill, and talk about basic food and drink.