"Do not swear at all: either by heaven, for it is God’s throne ..." (Matthew 5:33-37)

“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." (Matthew 5:33-37)

Is Jesus talking about cursing?

Note that the word "swear" is not referring to swear words, or what is commonly referred to as cursing.

The word "swear" is being translated from the Greek word ὀμνύω (omnyō). This means "to affirm, promise, threaten, with an oath" - relates specifically to making a promise upon something else.

For example, when we say "I swear on (fill in the blank) that this will happen," we are giving an oath, and swearing or promising on that particular (blank).

In other words, a more appropriate translation of the Greek word ὀμνύω (omnyō) would be giving an oath, or making a promise.

What does Jesus mean by 'people long ago'?

Jesus is speaking of the teachings of the prophets, who taught people in centuries past. This illustrates again the importance of time and circumstance within the teachings of the prophets including Moses.

Jesus is speaking of something specific taught by the prophets before him. While the exact statement is not in the current Old Testament, Jesus is likely paraphrasing this instruction by Moses:
When a man makes a vow to the LORD or takes an oath to obligate himself by a pledge, he must not break his word but must do everything he said. (Numbers 30:2)

No oaths at all?

Time and circumstance are relevant in Jesus' teachings in this regard. Jesus is instructing his followers not to make oaths as casual statements.

For example, a person might be debating with someone else, and will casually say, "I swear to God that I am telling the truth."

The key word here is thoughtlessly, as we find that Moses did discourage making oaths without careful consideration: 
"...if anyone thoughtlessly takes an oath to do anything, whether good or evil (in any matter one might carelessly swear about) even though they are unaware of it, but then they learn of it and realize their guilt..." (Lev. 5:4)
This means that if we were to appear in court and be requested to swear on the Bible: "I promise to tell the whole truth and nothing but the truth so help me God," that would not contradict Jesus' and Moses' teaching in this regard.

Or if we are asked to take an oath of office - that would also not be a "thoughtlessly" swearing by God.

Is this about one of Moses' Commandments?

Jesus is also mirroring one of Moses' instructions within the current time and circumstance so his followers can apply it specifically.

Casually swearing by God is another form of using God's Name in vain. This is also captured by the instruction of Moses:
“You shall not take the Name of the LORD your God in vain" (Exodus 20:7)
Only God has the ability to truly control events. When a person “swears by heaven” or “swears by the earth,” or “swears on his mother’s grave,” or “swears by God” to prove a point, these are oaths or promises that are using something that is sacred for materialistic purposes.

Jesus is clarifying that one should not utilize those things that are sacred - because of their relationship with the Supreme Being - for materialistic purposes.

Jesus is also recommending that his followers not utilize the Supreme Being's Holy Names or references out of context. He wants his followers to speak with honesty and sincerity about the things they know, and speak without duplicity.

The Holy Name of the Supreme Being has been cherished by God's loving servants since the beginning of time. Calling out, singing, or otherwise, the incantation of His Holy Names is an observance that can purify our consciousness and bring us closer to the Supreme Being. This is evidenced throughout the scriptures.

Who is the 'evil one'?

Who might this "evil one" be, who would be making promises that might not be able to be kept? Would this be another person besides ourselves? If we start making undoable promises can we blame someone else for it?

We cannot blame someone else. In fact, there is no word in the original Greek that can be translated to "one.” There is only the word πονηρός (ponēros), which means "full of labours, annoyances, hardships," and "bad, of a bad nature or condition: in a physical sense: diseased or blind," according to the lexicon.

Jesus is describing our diseased condition combined with the illusory nature of the physical world - the false pretense that we are these physical bodies and the forms and things around us belong to us.

This illusory energy reflects our self-centeredness. It reflects our desire to play the big man. We want to be supreme. We want to talk big - we want to seem in control. The illusory nature of the physical world - as we misidentify with these temporary physical bodies.

In other words, evil is the state of rebellion against God. Evil is the state of consciousness that says: "I don’t care about God, I’m going to go ahead and do what I want. I am powerful."

Is evil a form of rebellion?

Each of us is an individual and we each have the freedom to rebel against God if we choose to.

This is captured in the description of Adam rebelling against God in the Garden of Eden. We might want to blame someone else (Adam blamed Eve and Eve blamed the serpent). But each of us has the choice to follow God or rebel against Him. It is solely our decision.

This rebellion of the Supreme Being lies at the root of our descent into self-centeredness. Do we want to reawaken our spiritually and embrace love of God? Or do we want to continue to chew the chewed within materialism?

This is why we are here in the physical world. This is why we are currently away from God. We have been "cast out" of the spiritual realm and given these temporary physical bodies to play out our self-centeredness in an environment designed to teach us how to love.

Here we are given a physical body and a physical mind along with a forgetfulness of our true identity and past lives. This gives us the ultimate freedom of choice without bias.

Here we are given the opportunity to redirect ourselves towards reawakening our pure nature and embracing our relationship with the Supreme Being. We can chart a new course - one that fulfills the emptiness that currently plagues us as we seek true love and unconditional mercy in the wrong places.

This is what Jesus was sayiung when he taught:
“Very truly I tell you, no one can see the kingdom of God unless they are born again." (John 3:3)
Becoming born again is the act of having a change of heart. It is making a decision to utilize our life for the purpose of coming to love God and His children. This is a decision that any of us can make at any time.