Improvements

§ Human settlements survive on the natural resources available to them from nearby terrain. At first they may do this without "working the land" - they may glean nearby forests for nuts and berries, while hunters bring in whatever local animals are at hand. However, these local resources tend to be finite, and as a settlement's population expands they must improve their ability to gather sustenance or starve.
§ Over time, Man has developed sophisticated techniques for obtaining ever-increasing resources from the land. He builds farms to increase his food supply. He builds mines to obtain metals and fuels. He builds water mills to harness the power of rivers. He "improves" the land, making it capable of supporting ever-larger populations. In fact, Man's ability to gather greater resources with fewer people is the basis for all of civilization: if one man can create enough food for two, the second man is free to create writing, or paint a picture, or build a cathedral.
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Location of Improvements

§ Improvements directly benefiting specific cities must be within that city's City Radius, while improvements allowing your civilization access to certain Resources can be anywhere within your civilization's Cultural Borders (though it is usually good if they are also within a city's radius).
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Availability of Improvements

§ Many improvements can be built only in specific locations: mines, for instance, must be built on hills (or atop certain Resources), while farms can be built only where fresh water is available (until researching Civil Service). Further, all improvements have a technology requirement; for example, you cannot build farms until your civilization has discovered Agriculture. Finally, some improvements require that you have access to specific resources. Railroads require coal, for example.
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Workers

§ In Civilization IV, most improvements are built by Workers created in cities. These units cannot fight, nor can they create new cities, but they can build the farms, roads, and mines needed to support ever-bigger and more powerful cities. A civilization cannot flourish and grow without enough Workers.
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Work Boats

§ Work Boats are similar to Workers in that they can construct improvements on water; they can build fishing boats, whaling boats, and, later on, offshore platforms. There is one major difference between Work Boats and Workers, however; a Work Boat is consumed when it creates an improvement. You'll need to build one Work Boat for every at sea improvement you wish to accomplish. (Workers are not consumed when building improvements.)
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Constructing Improvements

§  To build an improvement, move a Worker to the space you want to improve. The actions available to that Worker are displayed in the "unit button" section of the main screen; if your civilization meets the technology and resource requirement for an improvement and if that improvement can be built on that space, it will appear in the Worker's unit button. Click on the improvement and your Worker will begin construction. (If the improvement is greyed-out, you cannot make that improvement at that time. Mouse over the improvement to see what you are missing.)
§ Constructing Roads and Railroads: You can build Roads and Railroads in one of two ways: you can manually build the road one space at a time, or you can use the "Route To" command, in which you click on "Route To" and then on the target space. The Worker will figure out the shortest route to the target space and construct the road to that space without further orders. (Beware: this method requires less work from you, but your Workers sometimes may not choose what you would consider the most optimal route.) See Movement for the effects of roads on movement.
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Time of Construction

§ Improvements take one or more turns to complete. Time of construction varies, depending upon the Civics you have in place, and certain Technologies will shorten construction time as well. Finally, two or more workers can construct the same improvement simultaneously, cutting the time of construction roughly in half.
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Interrupting Construction

§ You can stop working on an improvement at any time: simply click on the Worker building the improvement and give him new orders.
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Pillaging Improvements

§ Military units can destroy improvements in neutral territory or in the territory of a civilization you are at war with. To do so, move the unit to the target improvement and then click on the "Pillage" button (this will use up one of the unit's movement points). You may even be rewarded with plunder for your act of vandalism! If there are multiple improvements in a space (a road and a mine, for example) your unit will destroy one of them per turn. Note that roving Barbarians will happily pillage your improvements if they get the chance.