Learn Turkish: Garsonlar hızlı ve çok kibar. - The waiters are fast and very polite.

The word ve means "and". Just like in English, it links two similar things together. Here, it connects the two descriptive words: hızlı (fast) and kibar (polite).

Where is the word for "are" in Garsonlar hızlı ve çok kibar?

In Turkish, simple "to be" verbs like "am", "is", and "are" are usually attached to the end of a word as a suffix, or skipped entirely. For "they are", it is very common to just leave the adjective as it is. The fact that they "are" fast and polite is simply understood!

Since there is more than one waiter, why isn't it kibarlar?

Because the subject Garsonlar already has the plural suffix -lar, it is already clear that we are talking about more than one person. In Turkish, you usually don't need to add the plural suffix to the adjective at the end of the sentence if the human subject is already plural.

Does çok apply to both adjectives, making them "very fast" and "very polite"?

No, it only means "very polite". In Turkish, çok (very) describes the word right after it. Because it is placed after ve, it only applies to kibar. If you wanted to say "very fast and very polite", you would need to say çok hızlı ve çok kibar.