grammaticality - When to use a comma before coordinating conjunctions?

I understand that a serial comma (the one used before and/or) is used only when we have three or more items to be separated using and/or.

What exactly is the rule that governs where to add a comma before an and/or in a sentence such as the following:

• S1: I went to John's house, and I watched a movie there.
  


• S2: I went to John's house and there I watched a movie.
  


• S3: Look around for any evidence that might reveal the identity of the intruder, and carefully place that evidence in a plastic bag, so
  it can be examined closely at headquarters.

I have seen S1 written both with and without comma. Which is correct; why?

What would be the right way to punctuate S2; why?

Should there be a comma before so in S3 or not; why/why not?

Answer

Generally speaking, you want to use a comma in sentences made of two independent clauses connected by one of the following seven coordinating conjunctions: and, but, for, or, nor, so, yet.

Don't use commas between an independent and dependent clause UNLESS the dependent clause shows extreme contrast.

So, in the S1, there are two independent clauses connected by AND. Use a comma. In S2, again we have two independent clauses connected with AND. Use a comma. In S3, you have correctly punctuated the sentence according to the rules listed above (independent clause AND independent clause SO independent clause). However, you created a run-on sentence, so at least one of those clauses should be made into its own sentence.