I am getting confused with compound predicates and compound sentences. When do I need the comma. Would I leave the comma where I have it in this sentence: "Sally wanted to go fishing, but she didn't have anyone to go with."

I don't blame you for getting confused with that stuff. It's fine to leave the comma where it is, as it marks where two separate actions or thoughts are joined together by a conjunction (in this case the word 'but'). Personally, I also think it's OK to leave the comma out, as the lack of a comma would not make the sentence less understandable.

There's more on compound sentences here and whether to use commas here.