How do you form the perfect tense in French?

The perfect tense is used to talk about something that has happened in the past, usually an action that has completely finished (unlike the imperfect tense which often describes an action which is ongoing). To form it, there are three parts to the verb. First, the subject pronoun, for example 'je', 'tu', 'nous' or 'vous'. Secondly, the auxiliary, which is the present tense form of either avoir or être. Most verbs use avoir for the perfect tense, but there are roughly 17 which take être, for example aller, venir and arriver. Thirdly, the past participle. This is formed in regular -er verbs by removing the -er suffix and replacing it with é, for example, jouer --> joué. Regular -ir verbs remove the suffix and replace with i, for example, finir --> fini. Regular -re verbs remove the suffix and replace with u, for example, défendre --> défendu.
For example, to say I sang -- J' (I) + ai (first person singular of avoir) + chanté (past participle of chanter) = J'ai chanté
He went -- Il (He) + est (third person singular of être) + allé (past participle of aller) = Il est allé