Ray Liota Luagh

It's really easy, actually... "Der" is for masculine words, "die" for feminine words, and "das" for neutral words - all singular. For plural it's always "die". Thing is, you basically just have to learn whether a word is masculine, feminine, or neutral, because not all things that don't have an actual gender are neutral in German. For example, "der Tisch" (the table) is masculine even though it is a thing and "die Lampe" (the lamp) is feminine... But even animals can be a certain grammatical gender if it's not specified what actual gender they are. For example it's always "die Spinne" (the spider) unless it's actually important what gender it is. Same goes for "das Schaf" (the sheep). Sometimes there is one word for each, like "der Hund" (the dog in general, but also specifically a male dog) and "die Hündin" (when it's specifically a female dog).
Long story short, it's something you just learn with the word itself and have to remember.

Wow I can't believe I only just now saw your reply.
Thank you for that! I am actually an intermediate German speaker (I live in Germany), so I understand the principles behind the Der Die Das rules, but I do get a chuckle whenever I bring up a grammatical anomaly to a German and I usually get the reply "Well, that is correct, but it is actually a little more complicated than that...". Happens every time. Maybe next time I'll make one for Den Die Das, just to add to the pile.
But your suggestion is excellent for the beginners. Learners pay attention!

Well, German is a pretty old language and thus has warped and changed a lot and many of its rules have more exceptions than situations where they apply unaltered. It makes it fairly difficult to learn and most Germans don't even use it correctly. Since you live in Germany you might've heard of Bastian Sick who wrote several books on anomalies within the German language and common mistakes so many of us make daily that some of them have actually since been accepted as the norm by The German language standard: the Duden (the most famous/infamous example being the literal translation of "to make sense" - "Sinn machen", which is a construct that didn't exist in German until people kept using it so much that the Duden apparently got tired of claiming it to be wrong). I still consider them wrong but I'm in the minority with my prescriptive attitude (after all, why have rules when they get changed whenever enough people do it wrong?).