Donne tells the heavenly angels to fire up Judgment Day. Like the conductor of a symphony, he commands them to blow their trumpets in all parts of the world. The trumpets will awaken the souls of all dead people. The souls will be reunited with their bodies, like it says in the Bible.
Naturally, the collection of all deceased people in the world is going to include both good and bad folks. According to the Christian tradition, on Judgment Day, the good will be separated from the bad, which explains why the speaker wants everyone to wake up.
Then he tells God, essentially, "Wait, I didn't mean I wanted Judgment Day now. We've got to let those dead people sleep for a bit." Also, the speaker wants time to mourn for the dead and for his own sins. He worries that if he hasn't repented enough for his sins, he had better do his repenting on earth, before it's too late.
He asks God to teach him how to repent so he can be in the good category on Judgment Day. If God would only teach him repentance, the effect would be the same as if God had signed a pardon with his own blood. But here's the twist: according to Christian beliefs, God already signed this pardon (metaphorically speaking) when he sent Jesus to earth to shed his blood for humanity's sins.