When to use 想 versus 喜欢?
In short, 想 means "think (of)" when followed by noun phrases or clauses, and "want to" when followed by verb phrases, while 喜欢 simply means "like / be fond of" in all cases. 

Some details:


When followed by nouns/pronouns,


想 means "think of / consider" or "miss", for example:


  我在想你 = I am missing you; 我在想这个问题 = I am considering this question.

喜欢 means "like", for example:


  我喜欢你 = I like you


When followed by verb phrases,


想 means "want to (do)", for example:


  我想吃鱼 = I want to eat fish

喜欢 means "like to (do)" or "like (doing)", expressing non-momentary preference, hence not "would like to (do)", for example:


  我喜欢吃鱼 = I like eating fish


When followed by clauses,


想 means "think (that)", for example:


  我想他不会来了 = I think (that) he won't come.


Two relevant notes here:

a. When 想要 is followed by clauses, it doesn't mean "think (that)", but "want A to do", where A is the subject of the following clause, for example: 


  我想要他唱 = I want him to sing. 


BTW, a few native speakers may feel that 想要 in this usage is interchangeable with 想.

b. When 不想（要), in which "要" can be omitted, is followed by clauses, it doesn't mean "not think (that)", but "not want A to do", where A is the subject of the following clause, for example: 


  我不想（要）你来 = I do not want you to come.

喜欢 means "like it that", for example:


  我喜欢你这样做 = I like it that you do it this way