Comma Rule: Use a Comma After an Introductory Clause

Introductory clauses are dependent clauses that introduce the second part of the sentence.

Correct
After she finished shearing it, the sheep bought an expensive leather jacket to keep warm.
Unknown to the intrepid adventurers, the minions of the great magician Dave were on their trail.
These sentences are correctly punctuated because the comma separates the introductory clause from the rest of the sentence. 

That’s classic Dave to send someone to do his evil for him; Dave is very lazy, but he enjoys pointing at things.

Incorrect
After I woke up I went back to sleep.
Once I had woken up a second time I realized life was an endless cycle of waking up and falling asleep punctuated only by tiny and infrequent joys.
These sentences are incorrect because the comma does not separate the introductory phrase from the clause that is being introduced; it’s chaos! See how sad that second example was; that’s what happens when you don’t punctuate properly: sadness abounds. 

“No, mother, there will be no more music. I punctuated improperly, and life lost its flavor.”