How do you use 就 and 才?

就 and 才 are used to show when an action is earlier/ smoother/ easier than expected, or when an action is later/ more difficult than expected (respectively). They are both adverbs, so come just before the verb. This also means that they come after time and location in a sentence. For example, 她从朋友的家十点才回家了 (she didn't come home from her friend's house until as late as 10pm), or 两个人就能办好 (as few as two people can complete the job).

就 also has a few more functions in a sentence, always as an adverb. It can be used for emphasis, e.g. 他就是我的老师 (he is my teacher). It can also be used to link phrases. First, it can imply that one action happened immediately after another, e.g. 他下了课就去了图书馆 (he went to the library right after class). Secondly, it can show that one action happened as the immediate result of the previous action, as best seen in the 一...就 construction (where 一 acts as an adverb, translated as as soon as: 他一唱歌，我就哭 (as soon as he sings, I'll burst into tears). This can be used for general descriptions, whereas the first is only for specific occasions. It can also be used in a conditional sentence, often with 如果 or 要是. For example: 那本书太久了，我就把它扔了 (that book was too old, so I threw it away); or, 如果明天天气很好，我们就可能去公园吃野餐 (if the weather tomorrow is fine, then we can go to the park and have a picnic).