How do you know when to use que/qui instead of ce que/qui

Bonjour Helena,
That's a very interesting question indeed!
Let's point out first that we're talking about the relative pronouns here, which are used to introduce a new information in a sentence (as opposed to question words like "what?").

Once you know this, the separation is quite simple: "qui/que" can mean "who/which/that ..." whereas "ce qui/ce que" mean "what ...".

e.g. La fille que je regarde. (The girl whom[m]/that I'm watching.)
e.g. Je fais ce que je veux. (I do what I want.)

I hope that's helpful!

Precision: in cases where "ce qui / ce que" would also be translated by "which" in English, you need to ask yourself: What does "que/qui/ce que/ce qui" is referring to?
If it refers to a noun (expressed before), then you will use "que/qui".
If it refers to the whole part of the sentence, the whole idea, then it will be "ce que/ce qui".

e.g. Les gens que je rencontre ... (The people which I meet...)
Here "que" refers to "people"

e.g. J'aime les bananes, ce que tu trouves fascinant. (I love bananas, which you find fascinating.)
Here "ce que" refers to the whole fact that I love bananas, not just to the bananas

:)

Thank you!!! That was so clearly explained too - even if I'm confused in the future I now know how to figure out which one to use! :)

J'aime les bananes, ce que tu trouves fascinant. (I love bananas, which you find fascinating.)
Here "ce que" refers to the whole fact that I love bananas, not just to the bananas. . .
While I understand the explanation given, using the rule of thumb about following a noun, "If it refers to a noun (expressed before), then you will use "que/qui"." then que could also be correct, i.e. he finds bananas fascinating -- of course in reality that would be interesting that someone found bananas fascinating, like he/she had never seen a banana.
I do believe the better example is: "Je fais ce que je veux. (I do what I want.)"