How do I know when to use avoir and when to use être in the passé composé - the perfect tense?

The passé composé - the perfect tense - is used for talking about completed events in the past, such as 'I bought an apple', and it is formed using an auxiliary verb the present tense and a past participle. In the majority of cases, the auxiliary verb is avoir. Therefore, 'I bought an apple' would take the first person singular of avoir - j'ai - and the past participle of acheter - acheté: 'j'ai acheté une pomme'. Remember that there is no difference between'I bought an apple' and 'I have bought an apple' in French, and that the translation would remain 'j'ai acheté une pomme'.
However, in some specific cases, être is needed as the auxiliary verb instead of avoir. Etre is needed when you use reflexive verbs and verbs of movement in the perfect tense. A reflexive verb is where you must use a pronoun within the action, such as 'se lever' - to get (oneself) up. But what are these verbs of movement? They are any verbs that indicate a movement from one place to another, such as to go (aller), to enter (entrer) or to leave (partir), or changes in state, such as to die (mourir) and to be born (naître). Far fewer verbs use être, but it is crucial for your exam to know the important ones which do, because this is something examiners look out for. A way to remember some of the most important verbs which use être instead of avoir is the acronym 'Dr Mrs Vandertramp' - Devenir Revenir; Monter Rester Sortir; Venir Aller Naître Descendre Entrer Rentrer Tomber Retourner Arriver Mourir Partir. Although this looks like a lot, it is actually only sixteen verbs and a lot of them come in pairs which makes it easier to remember - rentrer and entrer, mourir and naître, for example! Also, remember that unlike the past participles when you use avoir, which stay the same for every conjugation, when you use être, you have to make the participle agree with the subject of the sentence. So for 'we got up', it would be 'nous nous sommes levés' (remember, it's a reflexive and so needs the reflexive pronoun), and for 'they (the girls) left', it would be 'elles sont parties'.