See wikipedia:Vermont for general information about Vermont.
Originally inhabited by Native American tribes (Abenaki and Iroquois), much of the territory that is now Vermont was claimed by France but became a British possession after France's defeat in the French and Indian War. For many years, the surrounding colonies disputed control of the area (referred to at the time as the New Hampshire Grants) especially New Hampshire and New York. Settlers who held land titles granted by these colonies were opposed by the Green Mountain Boys militia, which eventually prevailed in creating an independent state, the Vermont Republic, founded during the Revolutionary War and lasting for 14 years (although both NH and NY continued to claim it); Vermont is thus one of four U.S. states (along with Texas, Hawaii, and the brief California Republic) to have at one point existed as its own sovereign nation. In 1791, Vermont joined the United States as the fourteenth state, and the first outside the original Thirteen Colonies.
Vermont's 1790 census actually took place after statehood in 1791. Census coverage included virtually all settled portions of the State.
Many records are kept at the town clerk's office in each town. The Vermont Department of State maintains a list of the town clerks.
FamilySearch.org has a variety of collections available for free online:
Genealogical & Historical Societies
Outstanding guide to Vermont family history and genealogy (FamilySearch Research Wiki). Birth, marriage, and death records, wills, deeds, county records, archives, Bible records, cemeteries, churches, censuses, directories, immigration lists, naturalizations, maps, history, newspapers, and societies.
People at WeRelate Researching Vermont