"I forgot the password."
Chinese grammar lesson (of my own): How to deal with a language without articles
In a language with articles, like English, the definitive article "the" means that the modified noun is "the one in the current context". For example, in "I forgot the password", "The password" actually means password of my PC, bank account, or something else. But whatever, it is something both the speaker and the listener know. That is the "context". In some cases, the context is the world we live in. For example, "the sun". There is only one sun hanging in the sky, so nobody will get confused. In some other cases, it could be used to emphasize that the modified noun is the ONLY ONE that exists in our world. See the difference of "The god" and "a god".
The indefinitive article "a" means that the modified noun is "an arbitary one in the context". For example, When I say "give me a ball", I mean any ball that is in the listener's hands. Sometimes, The context is a category, and "a" indicates a general reference of the category. The sentence "A panda is an animal" means that every being in the category "panda" belongs to the category "animal" too.
There aren't any articles in Chinese. So all the related expressions must change. Here are the rules:
Definitive article "the"
just remove them.
I forgot the password. 我忘记了密码。
The earth orbits around the sun. 地球围着太阳转。(It's continuous tense, so technically it means "The earth is orbiting around the sun.")
Indefinitive article "a"
if what you mean is "an arbitary one". Then replace "a" with "one". And since you have a number now, don't forget the measure word!
Give me a ball. 给我一个球。
(The) panda is a kind of animal. 熊猫是一种动物。
If what you mean is a general reference of the category, remove "a" directly.
A panda is an animal. 熊猫是动物。
So how can we tell whether "a" implies a general reference or not? Easy. Try to change the modified noun to its plural form. "Pandas are animals" means the same, right? So you see that the number of pandas is unrelated to what you are trying to say.
This is a pretty good summary, and a good rough guide for translating between English and Chinese, but not entirely accurate with respect to the English.
"A panda" is essentially "any given panda", if you really want to use it as you have (instead of using "pandas"): "a panda would be able to climb out of this enclosure". It's "the panda" that denotes the general category: "the panda is a member of the bear family".
And "the god" is usually "the specific god to whom we've already referred", and not necessarily "the one god that exists", which we usually treat in English as simply "God".
In other words, "the" can indicate the thing taken as a generality, or it can indicate the specific thing to which we have already referred, or which is already understood by implication (as your first paragraph points out — "the sun" is indeed the sun in the sky that we all know, even though there are other suns in other solar systems...)
It's a little tricky and depends on context.