When and how was Plymouth Colony founded?

The Plymouth Colony was founded late in 1620, when the Mayflower arrived in Plymouth Harbor. The ship had been aiming for Jamestown, but ended up too far north. Because of a dangerously rocky coastline and bad weather, the colonists decided to stay put rather than try to head south.
The colony, though primarily associated in the American imagination with the Puritans (a group of Separatist religious dissenters who wanted to break away entirely from the Church of England), was actually a hybrid venture of Puritans and merchants. The Puritans sought religious freedom while at the same time wanting to maintain a distinctly English culture. The merchants who financed the journey, including Thomas Weston, saw the potential to make a large profit from establishing a colony in Virginia.
At that time, the Jamestown colony offered independent plantations to settlers. The Puritan new plantations (a plantation was a large tract of land and had nothing to do with slavery or what we would later think of as Southern plantations) would have existed under the general legal umbrella of Virginia, but would have been allowed to function largely independently and establish its own laws and governing bodies. When it became clear, however, that the group was nowhere near Jamestown and thus not under Virginia jurisdiction, the men on the ship established their own governing document, the Mayflower Compact.