If I want to say something like "I hate her", do I have to say "Je la déteste" or "Je lui déteste"? Could someone explain to me when one has to say "le/la" or "lui"? I don't really get it..

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It's "Je la déteste".

When the person is C.O.D. (complément d'objet direct = direct object complement), you use "le/la/les".
ex: I hate her. => Who do I hate? => her. It's a C.O.D. So, you said "Je la déteste".

When the person is C.O.I. (complément d'objet indirect = indirect object complement), you use "lui/leur".
ex: I give her flowers. => Who do I give flowers to? => her. There is a "to" in the question "Who do I give flowers to?", so "her" is a C.O.I.
So, you said "Je lui donne des fleurs".