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If you only use 讲究 alone, it's a verb that means you do things in a particular way, you don't do them casually or carelessly. And usually you need to follow some method, procedures and have certain knowledge and skill to do them well. For example, everybody in your town may know how to cook a local dish, but only the good cookers who 讲究 knows the right and good way to do it. If something 有讲究, it means that thing is created or done carefully. For example, in the sentence “张建”这个名字很有讲究 means the name "Zhangjian" is created with some special meaning in it.
If 有 is used before 讲究, then 讲究 is a noun. 有 of course means "have". So if something that you do requires you to have 讲究 if you do want to do it well.
Sometimes, 有讲究/讲究 doesn't necessary mean you will do them well or you good at it. In this case it just means you need to follow certain procedures and method to do it. For example, if you see a crazy person follow a strange but complicated procedure to tell people what will happen to them (like fortune telling) and you don't believe it or like it, you can also use 讲究 in a sarcastic way, such as 这疯子算命还挺讲究, to mean you find it even funny such nonsense is not mean to be done casually.
