"又 yòu" and "再 zài"
"又 yòu" and "再 zài" both have the meaning of "again" in English. There are three main differences between them though.
"又 yòu" is used for finished or completed actions.
我又到那儿去了。
Wŏ yòu dào nàr qù le.
I went there again.
你又说错了吗？。
Nǐ yòu shuō cuò le ma？
Did you say it wrong again?
"再 zài" is used for future events.
再说一遍。
zài shuō yī biàn.
Say it again.
明天你再来谈谈吗？。
Míngtian nǐ zài lái tántan ma?
Tomorrow will you come again to talk?
"又 yòu" can be used like "also" or "additionally". "再 zài" cannot.
我们是工人，又是学生。
Wŏmen shì gōngrén, yòu shì xuésheng.
We are workers and also students.
这个很好，又便宜吗？。
zhèige hěn hǎo, yòu piányì ma?
Is this one good and also cheap.
"再 zài" can show an idea of "even more". "又 yòu" cannot.
他再聪明也没用。
Tā zài cōngming yě méiyòng .
Even if he was smarter it would still be useless.
还有再大一点儿的吗？
Hái yŏu zài dà yīdiǎnr de ma?
Do you have an even bigger one?