There's no general rule.
Often, the gender is picked either from the ending (e.g. Romance words ending in -a may often be feminine, after the pattern of words such as "die Villa") or from a roughly-equivalent German synonym (e.g. "die Security" from "die Sicherheit"). Sometimes people disagree about the gender of new imports. ("der Blog? das Blog?")
Even words from English are not all neuter: der Sport, die Reling (from "railing"), der Service, der Manager, die Band (when pronounced "Bent" and referring to a musical group), ....
Yes, that's right: "die Pizza" is a feminine noun grammatically.
In German, all nouns have a grammatical gender, which can be either feminine, masculine, or neuter.
"das Messer" (the knife) is neuter, "die Gabel" (the fork) is feminine, "der Löffel" (the spoon) is masculine, for example.
No, not in general.
There are some endings that will usually indicate the gender (e.g. nouns ending in -heit -keit -ung -ion will usually be feminine), but for most nouns, you can't tell the gender just by looking at it.
Some nouns even have more than one gender, e.g. Leiter: "der Leiter" = leader, "die Leiter" = ladder.
Ich habe Hunger auf die Pizza.
In speech, you'd accent die because it means "that"; in writing, you can't tell the difference in that sentence except from context.
If you want to make it clear in writing, add a word for "there", e.g. Ich habe Hunger auf die Pizza da. "I'm hungry for that pizza there."
(This could also optionally be used in speech.)
It's one of the three grammatical genders that a German noun can have.
For example, das Messer "the knife" has neuter gender, die Gabel "the fork" has feminine gender, and der Löffel "the spoon" has masculine gender.
All three are objects, and have no natural sex or gender, but they do have grammatical gender in German. And the grammatical gender is not really predictable.
die is not "just an article" -- it's also a demonstrative determiner meaning "that" or sometimes "this".
diese means "this" but not (usually) "that".
So die Pizza can mean "the pizza" or "that pizza" or "this pizza".
(As a demonstrative determiner, it's usually stressed, so "that pizza" would be die Pizza -- but of course you can't tell the difference in writing.)
In English, "an" and "one" have separated, as have "that" and "the", but in German, there is only one word for each of them -- ein, eine is both number and indefinite article; and der, die, das is both demonstrative determiner and definite article.
Because it can.
The words used to be the same in English but split into "the" and "that" -- in German, the words still have both meanings.
So der, die, das can all mean either "the" or "that".
In speech, the stress will usually show what is meant (the words are usually unstressed in the meaning "the" but stressed in the meaning "that"); in writing, it's ambiguous or only clear from context.
If you really want to specify "that", then one option is to say "that ... there" (e.g. der Mann da, die Frau da, das Kind da).
I really hate this question. I mean, the only way to get this one wrong, is to mistype something, it's too obvious, and yet, this question comes up more than adjectives which I haven't learned all yet, or accusative case for masculine objects, which I always get wrong. I'd somewhat get if it was translating from english to german, as you'd have to know that it's "die" and not "der" or "das", but from german to english is nothing but the waste of time. This app is fun, it makes learning seem like playing a game, but there's too many basic questions and it can't differentiate between what you know and what you are struggling with. They need to do some sort of neural network on it, to create sort of an echo chamber, like facebook does with news, except that this would pester you with things you get wrong, instead of wasting your time on spelling the "wasser" 1000 times a day. I learned that one, ask me again in a week ffs. The mobile app is different but also fails. It when asking you to translate "the pizza" to german, offers you words like "die", "pizza", "Pizza", "Entschuldigung", "guten tag" and "maus". It basically gives you an answer. And it would give you a wrong if you select "die pizza" solely because of lower case "p" which I feel is irrelevant at this point of learning. It should instead give you words like "der", "den", "Pizza", "die" "Pizze" and "Pize" so that you actually have to pay attention and figure out which the is the right in this case.
Yes the pronunciation on this one is very poor
For der, die, das : I have noticed that (in addition to what others had already said): - most nouns seem to be masculine (der) - ones that could be either (eg: an egg - it could hatch out as a male or a female bird) are neuter (das) - so I focused on learning the feminine nouns and I try to 'guesstimate' the others