[subject] + 又 + [verb] + 了
[subject] + 再 + [verb]
[subject] + 想 / 要 / 能 + 再 + [verb]
[subject] + 还 + 想 / 要 / 会 + [verb]
又 + 是 / 要 / 该 + [noun] / [verb phrase] + 了
再, 又 and 还 can all mean "again" and all go before the verb. The split is whether the repeat has happened: 又 for a repeat that is real, 再 for one that isn't yet, and 还 for one asked about or intended.
又 usually takes 了 and often a note of annoyance. It also covers future events that are certain to come round – a weekday, a holiday, an exam – with 是, 要 or 该 and a final 了.
再 is for requests, plans and conditions. It follows a modal verb: 想再, 要再, 能再.
Under 没, 再 can describe the past: the repeat didn't happen.
还 does the job of "again" in questions about the future and before a modal verb – the opposite position to 再.
我想再去一次 and 我还想去一次 mean nearly the same; 还 adds that you've been before and want more. 还 can't take 了 with this meaning.
Asking for a repeat uses 再; complaining that it happened uses 又.