Learn French: Nous avons bavardé d'un jeu et nous avons chanté une chanson. - We chatted about a game and we sang a song.

This uses the passé composé, the most common past tense in French. To build it, you need two pieces: the helping verb avoir conjugated for nous (avons) and the past participle of the main verb. For regular -er verbs like bavarder (to chat), you simply drop the -er and add -é to get bavardé.

Why does the sentence use d'un to mean "about a"? Doesn't de usually mean "of" or "from"?

Yes, de often means "of" or "from", but it is also used after verbs related to speaking, like bavarder (to chat) or parler (to speak), to mean "about". Because un starts with a vowel, de un squishes together (elides) into d'un.

Why is nous avons repeated after et (and)? Can't we just say "Nous avons bavardé... et chanté"?

In English we often say "We chatted... and sang," dropping the second "we". In French, it is grammatically safer and much more natural to repeat both the subject and the helping verb (nous avons) for the second action.

I see chanté (sang) and chanson (song). Are they related?