The usual way to order anything is to say "Can I have ....?" or "Could I have ....?". You could add 'Please' at the end to be extra polite. The simplest way to ask for coffee with milk is to say "Could I have a white coffee, please?".
If there's a list of different coffees on the menu, you might see the word 'latte' ( pronounced 'lattay' - from the Italian word for 'milk') or cappuccino (pronounced cap-uh-chee-no), which is a frothy coffee with whipped milk. Some cafes offer extras like cream, chocolate or marshmallows on top.
You don't need to say whether you want sugar, as there are usually sachets of sugar available to add as you wish when you've received your drink.