どれ

どれ means "which one". It asks someone to pick one thing out of three or more. It is a noun, so particles follow it directly, and it never has a noun after it.

It is one of a set of four:

• これ – this, near the speaker
• それ – that, near the listener
• あれ – that over there, away from both
• どれ – which one

The answer points at one of them: これです, それです or あれです.

どれ vs. どちら

どれ needs at least three things to choose from. Between two, the word is どちら, or どっち in casual speech.

どれ vs. どの

どれ stands alone. In front of a noun the word is どの: ×どれ本 is wrong.

With particles

どれ takes the particle its answer would take.

どれが, not どれは

A question word cannot be the topic of a question, so ×どれは田中さんのかさですか is wrong. Either どれ takes が, or the thing you are asking about takes は and どれ comes after it.

Usage notes

These go beyond the plain question.

どれも and どれでも

どれも is "all of them", or "none of them" when the sentence is negative. どれでも is "any of them, it doesn't matter which".