Generally, 再 refers to some usages,
1, 再 refers to do something one more time or some more if the act has been finished, and once can be omitted sometimes.
E.g. 再唱一首歌=Sing one more song!
我明年要再去厦门=I'll go to Amoy once again next year.
2, 再 can also refer to continue doing something, if the act is not finished in the context.
E.g. 我想再多看一阵电视= I want to watch TV for a more while.
他还要再睡一会儿=He wants to continue his sleep for a little longer.
3, 再 implies a tone with uncertainty, the common phrases are 再看,再说,再等等
To be added。。。