どれ is from the same family of words as これ, それ, and あれ. These words are called こそあど言葉（ことば） in Japanese. Unlike the other 3, which all point to a specific thing, words starting with ど are designed for enquiring about something unknown. どれ can roughly be translated as ‘which’ in English, and is used for enquiring about a group (of 3 or more things).

• どれが飛（と）びますか。
  Which one of these flies?
• どれが新（あたら）しいですか？
  Which one is new?
• どれが綺麗（きれい）ですか？
  Which one is beautiful?
• どれが弟（おとうと）ですか？
  Which one is your brother?

From these examples, we can see that the particle が is often used with どれ, especially when preceding questions. However, when どれ follows a noun, は will be used.

• あなたの車（くるま）はどれ？
  Which one is your car?

When there are only two choices to select between, どちら + の, or どっち + の will be used instead of どれ. This is a habit that has become part of the language over time, and was not originally how these words were used.

• どちらのケーキを食（た）べますか？
  Which cake would you like to eat? (Out of these two choices)
• どっちのテストが難しい？
  Which test was hard? (Out of these two choices)