The perfect tense is used to describe completed actions in the past, and is formed in two parts. First comes the auxiliary verb (depending on the verb that you are putting into the past tense, this will either be "avoir" or "être"), which is then followed by the past participle of the verb. To determine your auxiliary verb, you follow a simple rule: in general, most verbs will take "avoir" UNLESS they are part of the DR & MRS VANDERTRAMPP acronym (Devenir, Revenir, Monter, Retourner, Sortir, Venir, Aller, Naître, Descendre, Entrer, Rentrer, Tomber, Rester, Arriver, Mourir, Passer, Partir). Once you have worked out which auxiliary verb is needed, it must be conjugated to match the subject of the verb (avoir = ai, as, a, avons, avez, ont ; être = suis, es, est, sommes, êtes, sont).
Next, the past participle is added. For -er verbs, the the -er ending is removed and replaced with -é. For -re verbs, the -re ending is removed and replaced with -u. For -ir verbs, the -ir ending is removed and replaced with -i. There are, however, exceptions to this rule where verbs have irregular past participles which must also be learned. Finally, it is worth noting that the past participle of verbs that use "être" as their auxiliary verb must agree in NUMBER and GENDER with the subject of the verb. For feminine subjects, an extra -e is added to the end of the participle, and for plural subjects an -s is added. For example, a group of females could say: "We went to the cinema." --> Nous sommes allées au cinéma.