Learn Turkish: Lütfen gürültü yapmayın.

Yapma is the informal, singular way to say "don't do it". By adding the -ın suffix (with a -y- buffer to separate the vowels), it becomes yapmayın. This is the formal or plural command form. Since the sentence starts with lütfen (please), the polite form is a natural fit.

Is gürültü yapmak the standard way to say "make noise"?

Yes! Just like in English, Turkish pairs the word for noise (gürültü) with the verb to do/make (yapmak).

Could this be written as yapmayınız?

Yes, you could say Lütfen gürültü yapmayınız. The -ınız suffix makes the command even more formal and is often used in public signs or official written announcements. Yapmayın is polite but a bit more conversational.

Why doesn't gürültü have an accusative ending like gürültüyü?

In Turkish, we only use the accusative case (adding the -yü) for specific direct objects. Here, you're asking people not to make any noise in general, not a specific noise, so gürültü stays in its base, dictionary form.