How do you know when to use AVOIR or ÊTRE when conjugating verbs in the past?

The answer is simply: you need to learn them and as you will progress through the course of your studies you'll know which ones take AVOIR and which ones ÊTRE. As a rule of thumb, most verbs in French conjugate with the auxiliary AVOIR. However, usually verbs of motion tend to use ÊTRE. For instance, try to remember the accronym: M->MONTER -to climb R->RETOURNER-to return S->SORTIR-to leave/to depart V->VENIR-to come A->ARRIVER-to arrive N->NAÎTRE-to be born D->DESCENDRE-to go down/to alight E->ENTRER-to enter R->RESTER-to remain T->TOMBER-to fall R->RENTRER-to go back in A->ALLER-to go M->MOURIR-to die P->PARTIR These are the most common verbs which you will come across in your GCSE, AS level and will have to be memorised.