Chinese has two words for "again". 又 (yòu) is for something that has already happened again. 再 (zài) is for something that hasn't happened yet: a plan, a request or a suggestion.
Subject + 又 + verb + 了.
Use 又 when the repeat has already happened. The sentence usually ends with 了. It often sounds a little surprised or annoyed, like "not again!" in English. The most common mistake is to use 再 here: 他昨天再来了 is wrong, because yesterday is in the past.
Subject + 再 + verb.
Use 再 when the repeat is still in the future. You will often hear it in requests and invitations, and with 一遍 or 一次 (one more time).
There is one case where 又 talks about the future: something that comes round again for sure, like a day of the week, a holiday or an exam. This 又 usually comes with 是 or 要, and the sentence ends with 了.
又 goes before words like 想, 要 and 没有: 他又没有来 means "he didn't come, again". 再 goes after 想, 要 and 能, directly before the main verb: say 我想再看一遍, not 我再想看一遍.
To tell someone not to do something again, use 别再 + verb + 了.
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