"The man drinks a beer."
Translation:Manden drikker en øl.
It is never "et øl", but there is a difference, I'll try to explain it. "En øl" and the definite form "øllen" means "a can/bottle of beer". When someone asks you "Vil du have en øl?" they mean a can or a bottle, like in this sentence.
EDIT: I see you're only at level 3, so the below is probably a little too advanced for you yet. I'll leave it just in case, but you only need to know right now that it is "en øl" :)
However, beer as a substance is uncountable, just like water or money; "one money" isn't correct, for example, it becomes "some money". Like with beer, "et øl" does not exist, but would rather be "noget øl". - some beer. Therefore, "øllet" is the definite form when talking about beer as a substance.
To illustrate the difference: "Øllen faldt på gulvet" - "the beer fell on the floor" means that the entire bottle or can fell on the floor, while "øllet faldt på gulvet" - same translation, means that only some of the substance itself fell on the floor, for example if you spilled a few drops.
Hope that clears it up (and doesn't cause any additional confusion)