The or no The

You generally need an article before a singular noun.  Your question should be written as follows:

Is there a simple rule to find out whether I should put an article before the next word or not?

There are a few exceptions - nouns that (for some reason) don't need an article. But you are still safe if you do use one.

I will attend university in the fall. 

I will attend the university in the fall.  

You can put it before plural nouns too. Some English determiners don't really take number, so it's only an issue if you use "a" with pluralized nouns. "I will attend the universities in the fall." or "I will attend a university in the fall." are both fine for me. Semantically, they might be a little weird, but you can still parse them.