Simple sentences have just one clause.
They may have additional phrases.
Example
I went to the park to eat a hamburger.
Juan, Daniel, and Sandra, my best friend from middle school, went to the movie theater and watched Harry Potter.
Two or more clauses joined with a coordinating conjunction.
Using commas between clauses is optional.
Example
I went home so I could get some sleep.
Doug did his math work but he got some wrong, yet he didn’t mind.
Two or more clauses joined with a subordinating conjunction.
If you begin a sentence with a subordinating conjunction, there MUST be a comma after the first clause.
Unless you want trouble, you should stop.
You should stop because I’m getting mad.
Has an independent clause and at least two dependent clauses, one of which is joined with a coordinating conjunction and one with a subordinating conjunction.
Examples
Because I paid attention, I got an A on the test and I was so happy.
I went home because it was getting late, but I had to wait on the porch until my mom got home anyway.