Good or no good
The four basic verdicts (good, OK, no good, bad) that answer 'is this all right?' about anything.
ii
polite ii desugood, fine, OK
いい いいです
The default positive verdict on anything, and 'fine, acceptable' when checking (kore de ii?). When choosing, X ga ii = I'd like X, and X de ii = X will do. It is also the core of -te mo ii (may) and -ta hou ga ii (should).
kore de ii?
Is this OK?
これでいい?
kore de ii desu ka?
Is this OK?
これでいいですか?
Only the dictionary form is ii; every other form uses yo-: yokatta, yokunai, yokute. As a reply, ii yo = sure, go ahead, but ii desu to an offer usually means no thanks; accept with onegaishimasu. Choosing a gift or dish, say kore ga ii: kore de ii sounds like settling.
daijoubu
polite daijoubu desuokay, fine, all right
大丈夫 だいじょうぶ 大丈夫です
Says someone or something is OK, safe or not a problem; it is how you check on people (daijoubu?), and daijoubu desu politely declines an offer.
kore de daijoubu?
Will this be all right?
これで大丈夫?
kore de daijoubu desu ka?
Will this be all right?
これで大丈夫ですか?
To an offer it usually means 'no thanks' (fukuro wa? / daijoubu desu), but it can also mean 'yes, that's fine', so clerks may check again. To accept clearly, say onegaishimasu.
dame
polite dame desuno good, not allowed
ダメ だめ ダメです
Says something is no good, won't work or isn't allowed (rules, plans, broken things, hopeless efforts), and is the base of -cha dame (must not).
kore ja dame?
Won't this do?
これじゃダメ?
kore ja dame desu ka?
Won't this do?
これじゃダメですか?
In the 'is this OK?' frame, de ii becomes ja dame: kore de ii? / kore ja dame?
warui
polite warui desubad, at fault
悪い わるい 悪いです
Bad in quality, weather, health (guai ga warui) or behaviour, and 'to blame' (X ga warui); the opposite of ii.
kyou, chotto guai warui n da
I'm not feeling great today.
今日、ちょっと具合悪いんだ
kyou wa chotto guai ga warui n desu
I'm not feeling well today.
今日はちょっと具合が悪いんです
Casual apology: warui! or warui ne (mostly male), and warui kedo... (sorry, but...), which everyone uses. The polite equivalent is sumimasen / sumimasen ga..., never warui desu.
Learn first: ii