Learn Turkish: Yeni komşumuz Alman. - Our new neighbour is German.

In Turkish, the "to be" verb for the third-person singular ("he/she/it is") is often invisible. While you could technically say Almandır, adding -dır usually sounds very formal, like an encyclopedia fact or a strong assumption. In everyday speech, just ending with the noun Alman perfectly translates to "is German".

Why do we use Alman here instead of a suffix like we do for Amerikalı?

Some nationalities in Turkish have their own special root words instead of taking the -lı or -li suffix (which means "from [country]"). Alman (German), Fransız (French), İngiliz (English), and Rus (Russian) are the most common examples. You wouldn't normally say Almanyalı for someone who is ethnically German.

If I wanted to say "Our German neighbour is new", how would the sentence change?

You would simply swap the words to: Alman komşumuz yeni. Because Turkish doesn't use a separate word for "is", the word at the very end of this kind of sentence acts as the main state of being. In Yeni komşumuz Alman, the final point is that they are German. In Alman komşumuz yeni, the final point is that they are new.