Learn Turkish: Çay, kahve ve su yok. - There is no tea, no coffee, and no water.

In Turkish, yok means 'does not exist'. You are literally saying 'Tea, coffee, and water do not exist.' Because you are making a group of the missing things, you use ve to join them together before applying yok to the whole list.

Do I need to put yok after every single item?

You could say çay yok, kahve yok, su yok to really emphasize that each thing is missing, but it is much more natural to list them together and put a single yok at the very end. The single yok applies to everything in the list before it.

Where is the verb 'is' in this sentence?

There isn't a traditional verb! Turkish doesn't use a direct equivalent for 'there is' or 'there are'. The single word yok completely covers the meaning of 'there is not' or 'does not exist', and it sits at the end of the sentence exactly where an action verb normally goes.

What if I wanted to say that there ARE tea, coffee, and water?

You would just replace yok with its exact opposite: var (there is / there are). Saying Çay, kahve ve su var simply means 'There is tea, coffee, and water.'