才 is kind of like the opposite of 就. i.e.我上午八点就来学校了- I'm came to school as early as 8:00am. 我晚上十一点才去睡觉了- I went to bed as late as 11:00. 才generally shows that an action is late(according to the speaker) such as: 你现在才去上班啊？you're going to work NOW?! [it's already past midnight] 你怎么现在才来呢？-why are you coming right now? [when you were supposed to be here hours ago] 又 means "again"and shows actions that has already happened but are happening/has happened again. 他昨天来学校又迟到了-he came late to class again yesterday. 我又吃了油条- I ate dough sticks again or 我又在看这部电影- I'm watching this movie again.

希望你能给出更具体确切的情况和场合啊，其实这两个字的意思是不一样的，但是经常用在一起，才字接的经常是刚才发生的状况和做过的事情，又字后面接的是马上接下来要做的事情或者是正在做的事情，比如我说，1.我才回家，你又叫我出去吃饭。 2.你才吃过饭，又要吃冰激凌，小心撑死哦。 这个才，和又，往往表现的是一种不情愿或者不太好的事情，表示不好的事情接踵而至。

前面的同学说得很多了，解释得很清楚了，我就不多说了。才表是刚刚，仅仅，强调。又表示再一次，还。语气不同，说话的人表达的意思是不一样的，非母语同应该注意区别。

ReTiger 的答案很不错，我很喜欢

才，as a meaning of "just", 我才去过somewhere. 又，means "again" ，我刚刚已经做过某事，现在又要再做一次。 most of time, 才 can bu used as a adv (in order to emphasize your sentences or your words) ,