Learn Hardcore German: Die Stadt ist wirklich laut.

In German, nouns have grammatical genders. Stadt (city) is grammatically feminine, which is why it takes the article die. You'll see this with other nouns too, such as die Schule (the school) or die Tür (the door).

What part of speech is wirklich in this sentence, and what does it mean?

Wirklich is an adverb here, and it means really or truly. It emphasizes the following adjective, laut, indicating that the city is not just loud, but really loud.

Why do we say ist instead of sein?

Sein is the infinitive form of the verb to be, while ist is the 3rd person singular present tense form. Since Die Stadt is a singular subject, you need ist as its verb form.

What does laut mean literally, and how else might you say the city is loud?

Laut literally means loud. You could also say Die Stadt macht viel Lärm (The city makes a lot of noise) or In der Stadt ist es sehr laut (It is very loud in the city). But laut is the simplest way to describe something as loud.