Since its is a possessive, it should normally be followed by a noun phrase -- you can't own a verb or adjective. The noun may be preceded by adjectives, which may be modified by adverbs. But there shouldn't be an article before it -- you say its color, not its the color.
Since it's is a contraction of it is, it should be followed by a phrase that can be used after the verb to be. This can be an adjective, optionally preceded by adverbs, when describing a quality that the object possesses. It can be a verb phrase, to describe something that the object is doing, or idioms like it's going to rain. It can also be a noun phrase beginning with an article, when describing what the object is, as in it's a book.
However, it's can also be followed by a noun phrase that doesn't start with an article, as in it's Fred's book or it's Washington, D.C. (the answer to the question What's the capital of the US?). It can also be followed by mass nouns, as in it's water, a noun phrase beginning with a determiner, as in it's his book. There are some special cases, such as
What's your favorite class in school? It's math. What's your favorite sport? It's football.
But you'll have to be very careful about some of this, because verbs can often be used as adjectives. Both of these are correct:
It's running late (referring to a train that's behind schedule)
Its running time is 90 minutes (referring to the length of a movie)