You can use again in expressions such as but again ,then again, and there again when you want to introduce a remark which contrasts with or weakens something that you have just said.
You can add again to the end of your question when you are asking someone to tell you something that you have forgotten or that they have already told you.
You use again in expressions such as half as much again when you are indicating how much greater one amount is than another amount that you have just mentioned or are about to mention.