This is often the only building you start out with, and you can usually only make workers or mining vehicles here that will then need to make everything else. As the game progresses, the headquarters often provides extra upgrades to increase some aspect of your units; giving them new abilities or providing them with enhanced stats.
Basic soldiers, usually there are several different types of these (general riflemen, rocket soldiers, flamethrowers). These are usually the first units you can make in the game and they are cheap to build, but often only effective in numbers. Some more covert units, however, like snipers, can go alone.
Not everyone on foot needs to be offensive-oriented; workers, medics, and engineers assist with building and repairing.
Initially, the first types of armored vehicles that are usually available to you are lightweight scouts that are fast but weak; and a more heavy, medium-sized vehicle like a tank. As you research more technology, advanced usually become available at the factory building, like heavy tanks, artillery, hovercrafts / amphibious vehicles, and mechs.
Naval docks often function the same way as factories, but restricted to water and making gunboats, submarines, and aircraft carriers instead.
The sky armor; jets, helicopters, and spacecraft. These usually follow a similar route as the ground armor - weak but fast fighters, medium gunships, and heavy bombers. Sometimes flying units need runways, landing pads, or aircraft carriers to station at when they aren't active.
Transport vehicles for land, sea, and air often have little or no means of attack, but can carry other units around.
These buildings provide you with some critical component to allowing you build more units and buildings. Power plants, mining shafts, and farms all give you more stuff to create more stuff to conquer your enemy with.
Research buildings usually don't build any units at all, but provide you with new abilities for units, or entirely new units to build at other buildings.
Support buildings provide some kind of direct assistance to you; for example, stationary turrets can provide extra defenses, a medical facility might heal nearby units automatically, or a shield generator might increase the defense of nearby units. Radar or sonar might let you see where the enemy is before he is in visual range.