Learn French: Ayons une bonne conversation au dîner. - Let's have a good conversation at dinner.

This is the imperative (command or suggestion) form of avoir (to have). While most verbs just use their normal present tense form for commands, avoir is irregular. To say "let's have", you must use the special irregular form ayons instead of avons.

How do we know ayons means "let's have" if the word "let's" isn't there?

In French, you create a "let's..." suggestion simply by using the nous (we) form of the imperative verb without the pronoun. So, just as allons means "let's go", the irregular form ayons means "let's have".

Why does bonne come before conversation? Don't most French adjectives go after the noun?

You're right that most adjectives follow the noun! However, short, common adjectives that describe Beauty, Age, Number, Goodness, or Size (often remembered as the BANGS rule) are exceptions and come before the noun. Bonne (good) fits into the "Goodness" category.

Why is it au dîner instead of just à dîner?

In English we just say "at dinner", but in French, meals are treated as specific nouns that need an article, like "the dinner" (le dîner). When the preposition à (at) meets le (the), they must combine into the contracted word au.