I have a coworker whose first language is not English. She is always asking me when to use "the" and when to use "a" or when to use nothing at all. This is instinctive for me, so I have a hard time explaining it to her. What is the rule?
First, the difference between 'a' and 'the' is that 'a' is an indefinite article, and 'the' is definite.
Can I have the apple you bought yesterday? (a specific one)
Can I have an apple? (it doesn't matter which one)
I am reading the book you recommended a few days ago.
I read a book because the TV programme was so boring.
As to the difference between 'the' and zero article see here:
Zero Article - Glossary Definition - UsingEnglish.com