On September 16, 1620, the Mayflower put out from Plymouth in Devon with 102 passengers and a crew of roughly 30, heading for the mouth of the Hudson River in what is now New York. They never got there. The ship made landfall at Cape Cod on November 21, after 66 days at sea, and dropped anchor inside the hook of Provincetown harbour.
The crossing should have taken a few weeks. It took more than two because the Mayflower had started late, in the wrong season, and because it was a cargo ship rather than a passenger vessel: a three-masted merchantman of about 180 tons, and the passengers lived between decks with about as much room as a person can lie down in. September was already late for a North Atlantic crossing. Storms in the mid-Atlantic sprang a main beam, and there is a well-known story that the repair was made with a great iron screw the passengers had brought along for a printing press. The beam held.
The passengers were not a single group. About 35 were Separatists, the English dissenters who had gone to Leiden in the Netherlands in 1608 and had decided that their children were becoming Dutch. The other 67 were recruited by the Separatists' backers in London: servants, craftsmen, and families, and they were called the Strangers then and now. The crew numbered about 30, and most of them stayed with the ship through the first winter.
Nobody was in charge of the Strangers once they landed. The patent they held was for Virginia, and they were outside it. That gap is what the Mayflower Compact was written to close, and 41 men signed it on November 21, the day they anchored, before anyone went ashore. It set up a government and asked for obedience to it.
The winter was hard. Half of them died. Only 53 passengers and about half the crew were alive by spring, and the survivors crossed the bay in December to the site that became Plymouth colony. The harvest of 1621, helped along by the Wampanoag, is what the Thanksgiving story is built on. The reason the voyage is remembered has more to do with the compact and the colony than with the theology that got the Separatists on board.