for one thing
Used in itemized lists or when giving a first reason; often followed by 二つ目, etc.
一つには時間がないし、二つにはお金もない。
For one thing, I don't have time, and for another, I don't have money.
Follows a noun to emphasize limitation; often used with だけ or しか.
残ったのは一つだけだ。
Only one is left.
(not) even one
Used with a negative verb to mean 'not even one'; emphasizes complete absence.
彼は一つも間違えなかった。
He didn't make even one mistake.
Adverbial use suggesting a casual attempt or small degree; often with ～してみる or ～してごらん.
一つ試しにやってみよう。
Let's just give it a try.
noun which may take the genitive case particle 'no'
some kind of; one type of
Used as a no-adjective to indicate a certain unspecified kind; often in 一つの～.
これは一つの解決策だ。
This is one kind of solution.
Please give me one apple.
For one thing, it's because there's no time.
There's only one wallet in this bag.
He doesn't tell even a single lie.
Let's just give it a try.
This too is one way of thinking about it.
一つ simply means 'one' (a single item), while 一つ目 means 'the first one' in an ordered sequence or 'one-eyed'.