It's funny that you mention it - I would say that using "the", "a" and "an" might be the most difficult task for me when I try to speak English. I tried to learn the rules but it seems to me that there are so many rules with so many exceptions that I am unable to get it right - it feels overwhelming and I am never sure whether I used it right or not. I cannot grasp the concept intuitively. Any trick to overcome this would be greatly appreciated.
The indefinite article ("a" or "an") is either a "pick from a collection" word or a new information marker in English. The definite article ("the") is either a specifier or refers to something that has already been introduced (old information, if you will). Think of "the" in most cases as a sort of weakened version of "that", and it may help. It is a subtle distinction, and one which may quickly become intuitive to a native speaker, but not one that a native speaker can always explain when asked. (Europeans generally have less trouble, but definite and indefinite articles are a European areal feature.) It doesn't help at all that the rules are often deliberately broken in literature to force the reader into a scene (usually by using a definite article for a first introduction, as if you'd known about it all along).
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.)
Chinese Mandarin has no the/a/an, and I believe most languages from the Sino-Tibetan family do the same. It is normally clear in the context anyway so (surprisingly) doesn't even lead to any confusion. They do have 'measure words' which can be used in a similar sort of function to a/an, but they are a bit more abstract.
My native language is Czech which is a Slavic language and we do have something similar to English articles. I think that sometimes it's more difficult to learn something that is kind of similar to what you are used to but not entirely the same - it gets really confusing.
