The Italian language knows a lot of kinds of "ci", the first and the second are the direct and indirect object pronouns, the third is the reflexive pronoun (ci = to/for us (indirect pronoun); ci = us (direct pronoun); ci = ourselves (reflexive pronouns).
Ci vedi?= Do you see us? (direct pronoun)
Domani ci porti la torta? = Do you bring us the cake tomorrow? (portare a = indirect object pronoun)
ci laviamo = we wash ourselves (lavarsi = reflexive pronoun)
"ci" can also replaces locations preceded by a, in, su, per, da
Vorrei andare in Italia. Ci vado domani. (replaces Italia)
Sei stato alla spiagga? Sí, ci sono stato. (replaces spiaggia)
Ci with the meaning of "at it/on it/ with it" (replaces additions with "a/su")
Pensi alle nostre vacanze? Sì, ci penso sempre.
Possiamo contare sul tuo aiuto? Sì, ci potete contare. (anche: Sì, potete contarci)
ci is used in a lot of idiomatic expressions
c'è / ci sono (there is, there are); C'era una volta... Once upon a time there was.... (the tipical beginning of every fairty-tale)
ci vuole / ci vogliono (it is required, necessary);
ci credo = I believe it. Potresti chiudere le finestre. Sì, ci penso io. (refers to the sentence)
by context. In this sentence it makes no sense to say: "we don't believe us".
The sentence: "La prima volta che non ci crederono", instead, can be ambiguous.
"the first time they didn't believe us" or "the first time they didn't believe it."
So you need the context to decide which would be the best translation.
It can also mean "each other", cant it (when the verb is not reflexive, i suppose)?, for instance: "Ci incontriamo". Then i wonder, too, if "Ci crediamo" could also mean "We believe each other", which, btw, is not accepted in this translation. Wondering also if "Ci laviamo" could also mean "We wash each other", or else how we would say the latter.
It occurs to me that in these cases we could say "Laviamo uno all'altro" and "Crediamo uno all/nell'altro" instead (to mean each other). Just my guess, unless we have to resort to the context in order to find out the actual meaning of "ci" in the sentence.
the reciprocal verbs are normally verbs that seems to be reflexive but involve more than one person or in other words.. verbs that describe actions ONE person could not do alone: baciarsi, incontarsi, vedersi, aiutarsi, conoscersi, parlarsi, salutarsi, scriversi, separarsi, telefonarsi
credersi = to consider oneself to be sth is reflexive.. . .. credere can also be used in a reciprocal way but in this case in Italian one would express it using "a vicenda"
ci crediamo a vicenda
In Italian normally you would use "a vicenda" to avoid confusion or ambiguity
ci laviamo a vicenda.. (ci laviamo would always be understood as there are more than one person and each one is washing himself...)