||1. As a copula verb (He is intelligent) it connects the subject with the predicative noun, in other words, it attributes the characteristic of the adjective / adverb to the subject of the sentence (We are intelligent, We are there) or establishes the identity between the subject and the predicative noun (He is a doctor). This used it mentionned first at Garzanti so we can deduce that as a copula verb mostly essere is used and not stare.
||1. In the sense of remain, stay. Allora, vai o stai? And now, to you stay or do you go?
||2. As an autonomous verb it describe the essence or nature of something (penso dunque sono, I think and therefore I am; to be or not to be, essere or not essere; stare o non stare would correspond more to stay or not to stay)
||2. In the sense of remain Stava lì, senza muoversi. He remains there without moving
||3. It describes the time or the climatic conditions (è Pasqua, it' s Easter)
||3. In relationship to things the place something is usually.
Il capotto sta nell' armadio. = The coat is in the cupboard.
stare a casa (to stay at home, decision). The difference between stare a casa and essere a casa is, that in the first case it is a decision.
You see the difference more clearly it you translate with different verbs.
He always stays at home. = Sempre sta a casa.
He is alway at home. = Sempre è in casa.
If the subject is a person the difference between essere and stare is more or less the same as between to be (essere) and to stay (to stay, to remain, to live)
Il libri che cerchi stanno sullo scaffale in alto. = The books you are looking for are above on the rack.
We already mentionned that stare is to be used if the position of an object relative to another object is to described. This contradicts to one example given by De Mauro ("La mia casa è tra il ponte e l' incrocio.My house is located between the bridge and the crossroad.) But De Mauro mentionnes as well a restriction. Only together with the prepositionsn (tra / fra) essere is used this way.
||4. It can be used instead of more specific verbs like avvenire (to happen): Sarà quel che sarà = Avverrà quel che avverrà; what will happen will happen
||4. Can have the meaning of to contain.
Nel nuovo stadio ci stanno 90 000 spettatori. = In the new stadium is place for 90000 spectators.
||5. In idiomatic expressions: "è possibile", "it is possible ".
||5. To describe relationships
Otto sta a quattro come dieci a cinque. = Eight behaves to four like ten to five.
||6. To describe a place or a state. Here we touch the Spanish "to reside at a place" which, as we already said, it not valid in Italian. Essere as well as stare can be used in this context, but with a subtle difference. With stare we describe the place an object (or a person) is usually, where it should be and with essere the place where it is at the moment of speaking. We have the description of a temporary residence as well in many metaphorical expressions (He groped in the dark = essere all' oscuro, to be in safety = essere al sicuro). All the examples below fits with rules mentionned before.
essere a tavola = to be at table
essere agli ordini di qualcuno = to be directly responsible to someone
essere al verde = to be out of money
essere dalla parte di qualcuno = to take someones part
essere in città = to be in town
essere in buona salute = to be in good health
essere nei guai = to be in the lurch
||6. In the sense of to live, to be located, to reside
Dopo la morte del marito è andata a stare con la sua figlia. = After the death of her husband she moved to her daughter.
7. In the sense of to be located
Il castello sta in cima alla collina. = The castle is located at the top of the hill.
8. To describe a physical state.
As it has been mentionned before very rarely stare is used with an adjective. In most cases stare together with an adjective is used if the adjective itself is ambiguous (Sono bene = I am good person, Sto bene = I am fine)
C' è chi sta peggio di te. = There are people worse than you.
9. With expressions of the type it is not good / bad
Non sta mai bene essere scortesi. = It is never good to be impolite
fare di queste cose assolutamente non sta bene = Do something like that is not good at all