1. In general, they are used more often in French than in English. The determiner indicates if a noun is singular or plural, so there usually must be a determiner (definite article, indefinite article, demonstrative determiner, possessive determiner, etc).
2. le, la, les -- when talking about a specific item (specific items). Je vois le chien. (I see the dog).
3. le, la, les, to refer to something in general. J'aime les chiens (I like dogs). L'amour est important. Love is important.
4. Instead of using possessive determiners with parts of the body, the definite article is used, along with a reflexive pronouns. Je me suis lavé les mains. I washed my hands (I washed the hands on myself).
5. Articles must be repeated if there is more than one noun. I see the dog and cat. Je vois le chien et le chat.
6. le, la, les - can translate as "per": Les épinards coûtent 2 euros le kilo. Spinach costs 2 Euros per kilo.
7. le, la, les -- form the superlative degree. les tomates les plus rouges - the reddest tomatoes. Without the second les, it's: the redder tomatoes.
8. possessive pronouns: le mien, les tiens, etc (mine, yours, etc) all require a form of THE.
9. dates: May 11 = le onze mai
10. habitual actions with days or times of day: Il travaille le matin/le mercredi. He works mornings/Wednesdays.
* -so, no definite article for one time days/times of day: Il travaille ce matin/mercredi. He works this morning/Wednesday. note: matin, still requires a determiner, just not the definite article.
11. with titles of people: Mr. President = Monsieur le Président
*but: if talking to a person with a title and a name, there's no def.article: Bonjour ministre Martin. Hello, Minister Martin.
12. in formal writing and/or speech, l' may be added to "on" or "un" simply to sound better. Not done in informal speech or regular writing.
13. note this: J'ai besoin de livres. I need books. J'ai besoin des livres. I need the books. books - is normally: des livres, but besoin - requires DE to mean OF (have need of) and so no definite article functions as a plural indefinite articles, translated by nothing in English. Using DES - is: de + les = of the books, a case where DES does not function as the plural indefinite article.
14.not also: pas de livre(s) = no book(s). pas les livres = not the books. pas le livre = not the book.
Hope that helps.
taught French; native English speaker