Just like other Japanese kosoado pronouns like these, we can separate these words like this:
- kore これ
This. (which is next to me)
- sore それ
That. (which is next to you)
- are あれ
That. (which isn't next to us)
- dore どれ
Besides the above, the expression are? あれ？, pronounced somehing like "ah-reh," can be used to express confusion, that is, you can translate it was "wat" in English. This is a entirely different meaning from "that" because the word has more than one meaning. That sort of thing happens.
Normally, however, are あれ is a pronoun that references something which isn't close to the speaker, which'd be kore, and isn't close to the listener, which'd be sore. It's used, for example, for something which both of them see, but neither hold.
Using Kore, Sore and Are
Unlike the pronouns kono, sono, ano and dono, kore, sore, ane and dore are used when the type of object being referenced doesn't matter. That is, if you're saying just "this," you sure kore, but when you're saying something like "this idiot" in Japanese, you have to use kono because it being an idiot matters.
- kore wa nani? これはなに？
kore wa nandeshouka? これは何でしょうか？
What is this?
(this phrase, for example, can't be used with the pronoun kono)
- kore wa omoshiroi これは面白い
This is fun!
This is interesting!
- kore wa dame da これはダメだ
This isn't good.
This won't work.
(see the meaning of dame)
- sore wa taberundesuka? それは食べるんですか？
Are you eating that?
Are you gonna eat that?
- sore wa ikenai! それはいけない！
That (which you're doing) shouldn't be done!
You shouldn't do that!
- sore wa iwanai hou ga ii それは言わない方がいい
It's better if you don't say that.
Don't say that.
- are wa akuma ka? あれは悪魔か？
Is that (over there, far from us) a demon?
- are wa ninja no waza jaanee あれは忍者の技じゃあねぇ
That (which we saw) wasn't a ninja technique.
Depending on the phrase, the meanings of kore, sore and are can get more complicated.
- kore de ii no ka na? これでいいのかな？
Is this (which I did) good enough?
- sore de ii no ka na? それでいいのかな？
Is that (which you did) good enough?
- are de ii no kana? あれでいいのかな？
Is that (which was done) good enough?
Are as an expression
And lastly, are as an expression (you'll notice it's often used with the particle ke け):
- are? kubi wo kittemo shinanai? あれ？首を切っても死なない？
Wha? [He] won't die even after cutting [his] neck?
- are? omatsuri wa kyou deshitakke? あれ？お祭りは今日でしたっけ？
Uhmm...? Was the festival today?
- are? yuurei no jakuten wa nandattake? あれ？幽霊の弱点はなんだったけ？
Wait... what was the ghosts' weakness again?
The word dore どれ is a little tricky, but that's especially because of expressions regarding the word. For questions regarding specific items, docchi どっち and dono どの are used instead, as dore often regards abstract objects or large number of items.
- anata no ie wa dore desu ka? あなたの家はどれですか？
Which (of these many, many houses) is your house?
(if there are only two choices, use docchi instead)
- dore demo ii どれでもいい
It doesn't matter which.
Whichever is good.
- dore kurai? どれくらい
- dore kurai ga kakaru no deshou ka? どれくらいがかかるのでしょうか？
How much is it going to cost?
- dore dake nokotteiru noka? どれだけ残っているのか？
How much is left?
(dore dake is used when you expect something to be diminishing)
- dore dore? どれどれ？
(expression used when tasting something or checking something out)