Explain how to use the passé composé.

The passé composé is used for actions which have been completed in the past.It is formed of an auxiliary verb, either avoir or être conjugated depending on the subject, and the past participle of the verb.
Most verbs use avoir as an auxiliary and is conjugated as follows: j'ai, tu as, il/elle/on a, nous avons, vous avez, ils/elles ont. So the passé composé is formed of this conjugation, plus the past participle. To form this, for 'er' verbs, remove the 'er' ending and replace with é, for example manger --> mangé. For 're' verbs, remove the 're' and replace with u, for example vendre --> vendu. For 'ir' verbs, remove the 'ir' and replace with i, for example finir --> fini. Here is an example of how to put this together. I swam --> j'ai nagé. They ate --> ils/ elles ont mangé.
For verbs of movement, or verbs which express a change of state or condition, we conjugate using être as the auxiliary. This is conjugated as follows: je suis, tu es, il/elle/on est, nous sommes, vous êtes, ils/elles sont.To remember which verbs this includes, we can use the mnemonic MRS VANDERTRAMP. These letters stand for: mourir, retourner, sortir, venir, arriver, naître, descendre, entrer, rentrer, tomber, rester, aller, monter, partir. For these verbs, the past participle must also agree with the subject - whether it's male or female and singular or plural.If it's feminine we add an 'e', and if it's plural we add an 's.' For example, if it's a group of men, the sentence 'they went out' translates to 'ils sont sortis'.Whereas if the subject is female, 'she went out' translates to 'elle est sortie'.