If you think it's hard in English, don't try to learn German then, grammatical cases are a pain in the butt.
A cat appeared on my back porch this morning. (New cat, no history at this point.) The cat then proceeded to shred the upholstery on every bit of furniture it could find. (We've already met the cat; using "a" in this sentence would introduce another cat.)
Of course John speaks a bit of Portuguese; he married a Portuguese woman. (We may have known John's wife for many years, but in this case she is merely one of a collection of Portuguese women. If we had used "the" in this sentence, it would imply that there is only one Portuguese woman in the world, or at least in the area, and that John married her.)
I am not a native English speaker so I may not be the best teacher of those details to a person speaking a different mother tongue than mine...