Who:
Dare (Donata)
だれ (どなた)

Who are you?
Anata Donata/Dare desu ka?
あなたはどなた/だれですか？

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What:
Nani
なに (何)

What is it?
Nan desu ka?
何ですか？

*With friends or close relatives, you can shorten the sentence to just 'Nani?'. (Informal form)

What is this?
Kore wa nan desu ka?
これは何ですか？

What is your name?
Anata no namae wa nan desu ka?
あなたのなまえ(名前)は何ですか？

For what, the 'i' in Nani is taken away when used in a sentence so it's just pronounced as Nan as seen in the above examples.

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When:
Itsu
いつ

When are you coming over?
Anata wa itsu kuruno?
あなたはいつ来るの？

When is April?
Shi-gatsu wa itsu desu ka?
4月はいつですか？

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Where:
Doko
どこ

Where is it?
Doko ni aru?
どこにある？

Where did you go?
Anata wa doko ni ikimashita ka?
あなたはどこに行きましたか?

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Why:
Nande
なんで (何で)

Why did you do it?
Nande shimashita ka?
何でしましたか？