As we have already said in the chapter before, ne corresponds in general to of it, about it.
ne = of it, about it
Do you have enough sugar? Yes, I have enough of it. Hai abbastanza zucchero? Sì, ne ho abbastanza.
Was he responsible for the accident? Yes, he was responsible of it. Lui era responsabile di questo incidente? Sì, ne era risponsabile.
Have you already talked about the topic? Yes, I have already talked about it. Hai già parlato di questo? Sì, ne ho già parlato.
More generally one can say that ne is used if we talk about a part of something.
Do you want some more coffee? Yes, I want some more. Vuoi ancora caffè? Sì, ne voglio ancora.
Have you talked about the problem? Yes, we have talked about it. Avete parlato di questo problema? Sì, ne abbiamo parlato.
The relationship to other pronouns is shown in the following table. (in Italian it is possible to add a pronoun, Me ne prendo => litterally: I take me some of it. This kind of dative is called dativus ethicus and is very frequent in Romance languages.)
Me ne prendo => I take some of it.
Te ne prendi => You take some of it.
Gliene prende => He takes some of it away from him.
Gliene prende => She takes some it away from him.
Ce ne prendiamo => We take some of it.
Ve ne prendete => You take some of it.
At least in realistic situations ne is never combined with a direct object, so there is no need to mention this combination.
That must be enough for the moment, we are going to talk about the pronouns once again later. At the moment we are only interested in knowing, where they must be placed. To explain that, we have to know all of them first. In the next chapter we are going to talk about the reflexive pronouns, then we have seen all of them.