Luckily, there is an easy way to remember which verbs take 'être' and which take 'avoir' in the perfect tense. You just need to learn the following acronym:
M - mourir
R - retourner
S - sortir
V - venir
A - aller
N - naître
D - descendre
E - entrer
R - rentrer
T - tomber
R - rester
A - aller
M - monter
P - partir
Usually, verbs that take 'être' are related to movement (leaving, going, arriving) of changes of state (being born, dying). Reflexive verbs - such as se réveiller, se lever, and so on - also take 'être'. All other verbs take 'avoir'. It is important to remember that the past participle of verbs that take 'etre' agree with the subject, so you might need to add an 'e', 's' or 'es' to the end of the word. For example: les hommes sont partis (the men went out), la femme est rentrée (the woman came back). Verbs that take avoir do not agree with the subject, so the ending is always the same: il a trouvé la voiture (he found the car), la fille a trouvé des crayons (the girl found some pencils).