To begin with, like other Japanese kosoado pronouns, you can divide these four words like this:
- kono この
This thing. (here, with me)
- sono その
That thing. (there, with you)
- ano あの
That thing. (over there, with neither of us)
- dono どの
(don't mistake the dono above with the honorific dono 殿)
On top of that, the ano あの can also be used to request someone's attention, like you're saying "hello? Excuse me? Are you listening? I'm here," and so on. This is, of course, a completely different meaning that has nothing to do with the usual meaning of ano あの, which'd be of referencing "that thing over there."
Examples of How to Use
These pronouns are like the pronouns kore, sore, are and dore, however, unlike them, the pronouns kono, sono, ano and dono are used to reference something of which the type or attribute is important enough to be mentioned or known.
So if "this" has an attribute that should be mentioned you use a pronoun kono, if it doesn't matter however you use the pronoun kore.
- kono baka! このバカ！
(here, baka 馬鹿 is an important attribute which must be duly noted)
- kono yarou! この野郎！
- kono keeki ga hoshii このケーキが欲しい
I want this cake. (not the other cakes, this one)
- kono subarashii sekai ni shukufuku wo この素晴らしい世界に祝福を！
Blessings for this wonderful world
- kono yo kara kiero! この世から消えろ！
Disappear from this world! (world of living people)
- sono kao wa doushita? その顔はどうした
What's with your face?
What's with that face?
Why that face?
- sono tame ni nandemo shimasu そのために何でもします
For that purpose (which you've mentioned just before) I'll do anything.
- sono kane wa doko kara detekitandesuka? その金はどこから出てきたんですか？
From where that money (which you have) came from?
- ano ken wa dou narimashita ka? あの件はどうなりましたか？
What became of that matter?
How did that turn out?
- ano yo ni okutteyaru あの世に送ってやる
I'll send you to that world! (Heaven or Hell)
- ano ouji-sama ga sonna koto! あの王子様がそんなこと！
That prince (emphasis, not other princes, THAT one) did such a thing!
Ano meaning as an expression
As I said, ano can be used as an expression too, so here's an example of that case:
- ano... sumimasen, dareka imasu ka? あの～すみません、誰かいますか？
Hello? Excuse me, is anybody there? (here, home, etc.)
Using Dono どの
The pronoun dono どの is mostly used in expressions in Japanese and you're more likely to find docchi or dore used to ask "which" or "what" instead of dono.
This is because you have to say the attribute of what you're talking about after the word dono, but in most cases this attribute is already known from the context of the question, so you don't really have a need to say it.
It's like saying "which do you want?" or "which flower do you want?" If you're already talking about flowers you don't need to use the word flower, so you wouldn't use dono, you would use docchi instead.
- dono manga ga suki desu ka? どの漫画が好きですか？
Which manga do you like?
- dono pokemon wo sodatereba ii no? どのポケモンを育てればいいの？
Which pokemon should I raise? (tame, train, level up, etc.)
- tsugi wa dono anime wo miru ka na? 次はどのアニメを見るかな
Which anime I'll watch next, I wonder?
- dono youna goyouken deshouka どのようなご用件でしょうか？
What is the matter?
What brings you here?