"The book is in New York."
Translation:Liber Novi Eboraci est.
The locative case is being used here, and it does not take any prepositions.
There is this plain-English overview of what the cases are and how they work:
Latin cases, in English
Adjectives must agree in gender, number, and case with the nouns they modify, but they have their own declensions. Sometimes you get lucky and the adjective just happens to follow the same declension as the noun, but that is not a guarantee.
There are these conjugation charts:
Latin verb forms