There are thousands of records, dating from ancient China, the Babylonians, the Egyptians, the Greeks, on up to the present day. It was Edmund Halley who thought that repeated views 76 years apart were the same comet. His was a periodic one. Some never come back, some decay into gravel and dust to become meteor showers.
The origin of most comets is thought to be a giant hollow sphere around the Solar System, way out beyond Pluto. There might be billions of ice balls out there, dark and frozen. They are not huge then, but only a few miles across at largest. Only when a passing star disturbs this Oort Cloud that some fall toward the sun. As they heat, a cloud of gas and dust thousands of miles across forms, then a tail millions of miles long. A lot get captured by Jupiter (like Shoemaker-Levy9). Some graze the sun, like Hyakutake or Ikeya-Seki. Some could be seen in daylight, like McNaught. Some are hanging in space opposite the sun, like Lulin, right now next to Saturn and Regulus.