Rule 1: Capitalize north, south, east, west, and their derivatives when belonging to proper names or when used to signify specific regions: I live in the North, North Pole, Southern Hospitality, West Coast, down South.
Rule 2: If the words indicate a direction, do not capitalize them: I lived in the south of Germany, drive west on this road until you hit the stop sign.
Rule 4: If preceding a location, lowercase the attribute unless it is part of the name: northern New York, Northern Ireland, western Germany.
You might have noticed a trend among these rules: capitalize proper adjectives and lowercase improper adjectives. Allow me to explain; proper adjectives have more class, money, and refined manners. In other words, proper adjectives are ones that refer to or belong to nouns. France is a noun, and French is a proper adjective, because it refers directly to the preceding noun. I lied about the manners.