Avoir is irregular in almost every tense and mood. It literally means "to have," but it also works as an auxiliary verb and shows up in dozens of everyday expressions, several of which English speakers get wrong at first, simply because English uses a completely different verb for the same idea.
1. Avoir = to have, to possess
The most literal meaning; this one works just like English.
| J'ai une voiture bleue. | I have a blue car. |
| As-tu un chien ? | Do you have a dog? |
| Nous avons deux enfants. | We have two children. |
2. Avoir = to be, the #1 trap for English speakers
In a whole family of common expressions, French uses avoir exactly where English uses "to be." This is probably the single most common mistake English-speaking students make when they start out.
| J'ai faim. | I am hungry. (literally: I have hunger) |
| J'ai froid. | I am cold. |
| Il a raison. | He is right. |
| J'ai 15 ans. | I am 15 years old. |
3. Avoir as an auxiliary verb
For most French verbs, avoir is also the helping verb used to talk about the past. You'll see this a lot once you start using the passé composé.
| Nous avons déjà mangé. | We've already eaten. |
| Elle a visité Nice. | She visited Nice. |
4. Conjugation, present tense
| j'ai | I have |
| tu as | you have (informal) |
| il / elle / on a | he / she / one has |
| nous avons | we have |
| vous avez | you have (formal / plural) |
| ils / elles ont | they have |