"The man drinks wine."
Translation:L'homme boit du vin.
In French "du" is called a partitive article. It roughly means "some" but in English we usually use no article in it's place.
The easiest way to get started is to realize that almost every noun needs an article. There are 3 types of articles:
Partitive - "He eats [some] cake"
Definite - "He eats the cake"
Indefinite - "He eats a cake"
I put the some in brackets because it's usually dropped in English so you don't normally see it, but roughly speaking it can be included. In French the three ways of addressing a noun have the following equivalents:
Partitive - "Il mange du gâteau"
Definite - "Il mange le gâteau"
Indefinite - "Il mange un gâteau"
It takes a while to get used to, but hopefully that will get you started.