How do you know whether a verb takes avoir or être in the past tense?

Most verbs in French take 'avoir' in the past tense e.g. manger --> j'ai mangé. However, there are 14 verbs that take 'être' in the past tense and these can be remembered using the DR MRS VANDERTRAMP mnemonic:Devenir (to become)Revenir (to come back)Monter (to go up)Retourner (to return)Sortir (to go out)Venir (to come)Aller (to go)Naître (to be born)Descendre (to go down)Entrer (to enter)Rentrer (to go home/to return)Tomber (to fall)Rester (to remain)Arriver (to arrive)Mourir (to die)Partir (to leave)
So rather than saying "J'ai devenu" we have to say "Je suis devenu" because we know that devenir is a DR MRS VANDERTRAMP verb. The important thing to remember is that verbs that take être must AGREE. Whether you are talking about a boy or a girl, or one individual or a group of people, 'I ate' will always be "j'ai mangé". By contrast, "I went" will be 'je suis allé' if you are a boy but 'je suis allée' if you are a girl. 'We (a mixed group) left' would be 'nous sommes partis' but 'we (a group of girls) left' would be 'nous sommes parties'. The only other verbs that take être in the past tense are reflexive verbs - typically routine verbs e.g. to wake up (se réveiller) - so I woke up = Je me suis réveillé(e).