When do I use être or avoir in the past?

Etre is used with verbs of motion such as Aller/Entrer/ Arriver. The full list is easy to remember using the MRS VANDERTRAMP technique.

M-Monter
R-Retourner
S-Sortir
V- Venir
A-Arriver
N-Naître
D-Descendre
E-Entrer
R-Rester
T-Tomber
R-Rentrer
A- Aller
M-Mourir
P- Partir

All other verbs take avoir.