Like AlexisLinguist said, there is a set of rules in the "Tips Notes" section of Basics 1 that explains it.
But usually, de is usually used for nouns with gender, like man, vrouw, and jongen. Het is used for genderless (neuter nouns), like boek.
Meisje is an exception because it ends with a -je (it's a diminuitive). So instead of de, you say Het meisje. :)
native dutch here.
dutch rule about the word "het": with words ending on -je you always have to use het.
the rule with de, het and een is difficult to explain, becouse its a very old rule. we forgot why it is there,but we also cant remove it, becouse its an every day thing for us. if you see an word with de and het, you have to try to remember it.
Apparently there are apps for iPhone and Android which can help, but I haven't tried them.
Here are some guidelines for het:
Diminutives: boompje, tafelje, glaasje;
Names of languages: Duits, Chinees;
Names of countries and places: het multiculturele Nederland, het Irak van voor de oorlog;
Metals: aluminium, goud;
Compas direcitons: zuiden, noordoosten;
Sports and games: voetbal, poker, biljart;
Nouns with two syllables having prefixes be-, ge-, ver- and ont-: beslag, gebit, verslag and ontzag;
Nouns with suffixes -isme, -ment, -sel and -um: kapitalisme, abonnement, stelsel and aquarium; however: de or het mengsel, de cement.
In German, where there are actual noun genders as opposed to Dutch, "das Maedchen" is neuter (and also formed with a diminutive -"chen"), as opposed to taking the feminine article "die." If you have had any exposure to German, that is a way to remember. I have yet to pick up on it completely but there does sometimes seem to be a clue from German on what to do.