Die, Der, Das for no gender objects.
Das would be used for neutral nouns, as der for masculine and die for feminines. Why is it when you say The Newspaper it's Die Zeitung, using feminine and Der Apfel, using masculine. Even weird Das Wasser as neutral. Even though these noun objects have no gender, it seems like you do place one. I'm a bit confused on that.
Always learn the noun together with the article and the plural form, because these are mostly arbitrary, so you need to learn them together. So for example for the word "dog" learn this: der Hund, die Hunde (masculine noun and plural is Hunde)
It's more or less arbitrary and you have to learn them by memory. There are some rules of thumb, though. Any word that ends in -chen like Mädchen (the girl) is neuter (das). So yes, it's das Mädchen, NOT die Mädchen. See this for some more examples: http://backword.net/german/german_gender_guessing.html I've also read somewhere that masculine is the overwhelmingly most common gender, so when in doubt, guess masculine. Also here http://german.about.com/library/blgen_der.htm is good.
You have to distinguish between the grammatical gender of a word (indicated by "der", "die", "das") and the biological sex. In German, these things have very little to do with each other. Of course an apple is not male in a biological sense, but it is grammatically male all the same. When talking about people, grammatical gender and biological sex are usually the same (but even here there are exceptions: das Mädchen (the girl) is grammatically neutral). Sometimes the grammatical gender can be deduced from the ending of a word, but very often it's completely arbitrary. In French, the sun is grammatically male and in German it's female. Why? We'll never know - these things just have to be memorised.