When not to use an article:

To indicate a profession Il est docteur. He is a doctor.
Elle est avocate. She is a lawyer
Il est devenu infirmier. he became a nurse.
Elle est devenue mère au foyer. She became a stay-at-home mom.
adverb + de + noun/adjective
Il a beaucoup de problèmes.
il n’a pas de chaise. He has alot of problems.
he doesn’t have any chair.
le résoudre d’une problème. The solution of a problem
verb+ quantity + noun Elle a reçu plusieurs invitations. She got several invitations.
After some prepositions when talking in a general way
chercher-to search/ to look for
avec -with Elle cherche un appartement avec balcon. She is looking for an apartment with a balcony.
sans-without Elle cherche un appartement sans balcon. She is looking for an apartment without a balcony.
sous- under L’Europe est sous eau.
le chat est sous table. Europe is under water.
en - in …. Nous sommes en classe. We are in class.
par- by Il fait ça par habitude. He does that by habit.
After “ne… ni… ni…’’ - neither - nor Je n’ai ni stylo ni cahier. I have neither pen nor notebook.
After parler- to speak
when talking about languages (optional) Je parle (le) français depuis quelques années. I have been speaking French for a few years.
Il aimerait parler (l’)espagnol. He would like to speak Spanish.
Before meals (sometimes) Nous avons pris (le) dîner à 19h. We had dinner at 7 p.m.

Les articles partitifs become — de before adjectives
des films — de bons films ( good films)