"Your newspaper is good."
Translation:Eure Zeitung ist gut.
There are differences between them.
1) informal, talking to one person: "dein" (your). The corresponding personal pronoun "you" is "du".
2) informal, talking to more than one person: "euer" (your). The corresponding personal pronoun "you" is "ihr".
3) formal, talking to one person or more: "Ihr" (your). The corresponding personal pronoun "you" is "Sie". [Note that the formal possessive article "Ihr" (= your) is capitalized here to distinguish it from the informal personal pronoun "ihr" (= you) in 2)].
Basically, you use the informal forms when talking to friends and family members and the formal forms when talking to anybody else. In practice, it's a bit more complicated than that but that's the basic idea.
The endings of all the possessive articles, i.e. terms for "your" (dein, euer, Ihr), change depending on the gender, case and number (singular/plural) of the following noun, e.g. "DeinE Zeitung ist gut". So you first have to decide which of the three forms to use and then add the appropriate ending.
First, it should be "DeinE Zeitung" because Zeitung is feminine.
As for "gut". There are two different types of adjectives:
a.) attributive adjectives, i.e. adjectives before a noun. They get a special ending. Ex. deine gutE Zeitung (your good newspaper)
b.) predicate adjectives, i.e. adjectives used on their own after the verbs "sein" (to be) or "werden" (to become). They get no special ending. Ex. Deine Zeitung ist gut. (Your newspaper is good). http://coerll.utexas.edu/gg/gr/adj_02.html
Here, we're dealing with a predicate adjective, so there is no special ending: Deine Zeitung ist gut/Dein Mann ist gut/ Dein Buch ist gut. Since it's a predicate adjective, the basic form "gut" remains the same for all genders.