I watched Code Geass, and now I want to know: How did Geass come into existence? Who or what created Geass?
Answering your question to the letter,
a Geass is created when a code user makes a contract with a human.
The type of Geass and its specific powers are dependent on the Code user, the new Geass user's personality and other specifics that are not discussed in the canon material.
But I feel like your question is not about how Geass powers comes into being, and more in the lines of how the superpowers of the characters (Geass and Code) come into being.
The backstory of the Code users is not revealed in depth. The further back we are shown is the life of C.C. while still mortal when she receives the Geass from the catholic nun.
(screenshot of C.C. and the nun)
While the epoch is not revealed, it is supposed to be in the High Middle Ages, circa XIV century (before the Age of Discovery) if I had to guess (and yes, this paragraph is pure guessing).
The reason I am assuming that C.C. backstory happens before the Age of Discovery is that she was already immortal for quite some time and was with George Washington and Benjamin Franklin during the American revolution (1700'), as shown in a special feature in the DVD release. Remember that in the world of Code Geass, Ben was granted nobility, betrayed Washington, and America was never independent form Britannia.
Since the nun was already immortal and already willing to give up immortality and die, the same state of mind C.C. is when she meets Lelouch, we can assume the nun is at least half a millennia old (around the same "oldness" as C.C. when the series launch).
So the codes should be around for at least a millennia. There is no info as to who the people with code sigils in their foreheads are, or how old the Geass order is. But one can assume that for as long as codes were around, Geass users are too.
(screenshot of the code people)
You could dig the origin of the term Geass (geis) on the internet (Wikipedia), but word of god never discussed this far back in the fictional world.
The timeline of the fictional world is here: world of Code Geass, but it does not go into the powers, only historical facts. Whether Geass was used or not in these events (like geassing Ben Franklin into betraying George Washington), it is not discussed.
That was not explained in the anime, but it was kind of explained in the OVA.
When people crave for power to change the reality, one day they are starting to have that power. It is granted by collective consciousness (in OVA), or how we call it in the real world: Prima Materia or Chaos. It originated around that time when first abstract intelligence evolved (so long LONG time ago, before written history).
I think that my answer is quite accurate, even if it is not based solely on the Code Geass. Note, that Geass comes from Geis, which comes from Arianrhod, which is not in anime anymore, but in Celtic religion. Still, Chaos or Prima Materia was first described in writings (hieroglyph "kh") by ancient Egyptians long, long time ago.
My guess is that Geass was an isolated high order of beings that existed before human civilization became a norm. I came to this conclusion from seeing Charles activate the Ragnarök Connection from all of the world’s ruins. Using humanity’s beginnings to bring about its ultimate destruction and rebirth.