Well we talked to the minister beforehand and turned it into the courthouse ourselves. The day after the wedding, we were married on a Sunday.
Usually, the minister, or whoever, mails it off and then it gets to the courthouse and then it gets mailed to you.
You can take it yourself and pick up a copy yourself and it takes a lot less time. If we had been married on a weekday and dropped it off that day we could have picked it up the next morning.