Starting by saying that, like in English, the auxiliary
1. essere/to be usually recalls a passive form (where the action is "experienced" by the subject)
and
2. avere/to have an active one (which is part of composed tenses like past participle and so on, and which sees the subject acting and not bein subjected to),
in order to know which auxiliary use (when one is mandatory or not) you should make reference to a dictionary.
At examples:
scendere
http://www.treccani.it/vocabolario/scendere/
scéndere v. intr. e tr. [tratto da discendere, per riduzione di prefisso] (io scéndo, ecc.; pass. rem. scési, scendésti, ecc.; part. pass. scéso; come intr., aus. essere). –
like intransitive verb, auxiliary to be
come intr., aus. essere
correre
http://www.treccani.it/vocabolario/correre/
aus. essere quando l’azione è considerata in rapporto a una meta, espressa o sottintesa,
to be when the action is considered in relation to an, expressed or implied, destination
vivere
http://www.treccani.it/vocabolario/vivere/
aux to be, and with some acceptations to have
finire
http://www.treccani.it/vocabolario/finire/
And so on.
Look only for the best, truthful sources...