Again, you have heard that it was said to the people long ago, 'Do not break your oath, but keep the oaths you have made to the Lord.' But I tell you, Do not swear at all: either by heaven, for it is God's throne; or by the earth, for it is his footstool; or by Jerusalem, for it is the city of the Great King. And do not swear by your head, for you cannot make even one hair white or black. Simply let your 'Yes' be 'Yes,' and your 'No,' 'No'; anything beyond this comes from the evil one.
I believe that this passage is less about oaths and swearing, and more about your words. As citizens of the Kingdom of God, every word we speak should be an oath. We should be the speakers of truth. And our words should be so true that there will be no need to swear. You could rephrase the last part as, say what you mean and mean what you say.
This is a difficult thing in a world filled with triviality, excuses, and sarcasm. Our words should be well placed words.
As you go through your day today, ask yourself if your yes means yes and your no means no.
Also note how powerful and cutting Jesus' words are. (Remember that his yes means yes and his no means no...) At the end of the verse he says, "anything beyond this comes from the evil one. If I went around saying this, I would be called harsh, critical, and judgemental. How dare I say that anyone's actions come from the evil one?!?
But Jesus speaks it and He means it.