Most buildings are workplaces where your units manufacture goods. A brand new colony begins with a few basic buildings. Hammers and Tools are used to build new ones. Some buildings serve other purposes; see below.
The Town hall cannot be upgraded. It produces liberty bells by itself if your population is below 3. The Printing press and Newspaper increase your liberty bell production (in the Town hall); they do not directly employ workers.
Docks may only be built in coastal colonies; they allow you to work on water tiles to produce Fish, which become Food. A Drydock lets you repair damaged ships (without one, they will be repaired in Europe), and a Shipyard lets you produce your own ships. These buildings do not directly employ workers. Fishers work on water tiles, and ships are built with Hammers and Tools.
A Stable allows you to breed Horses. You must have at least 2 Horses to begin with (they must be purchased in Europe initially). Horse production requires Grain, and reduces the amount of Food going toward your population increase.
A Schoolhouse, College or University lets your specialist units teach their skills. These buildings support 1, 2 or 3 simultaneous teachers, respectively. Each teacher may have 1 student at a time. Any skill may be taught in a University; most can be taught in a College; and only the simplest in a Schoolhouse. A Free Colonist may learn any skill this way. An Indentured Servant may become a Free Colonist, and a Petty Criminal may become an Indentured Servant (both of these upgrades are independent of the teacher's specialty).