Dry Systems
In a "Dry" nitrous system, extra fuel required is introduced through the fuel injectors, keeping the upper intake dry of fuel. This property is what gives the "Dry" system its name. Fuel flow can be increased either by increasing the pressure in the fuel injection system, or by modifying the vehicles' computer to increase the time the fuel injectors remain open during the engine cycle. This is typically done by spraying nitrous past the MAF sensor (Mass Air Flow), which then sends a signal to the vehicles computer telling it that it sees colder denser air, and that more fuel is needed. This is typically not an exact method of adding fuel. Once additional fuel has been introduced, it can burn with the extra oxygen provided by the Nitrous, providing additional power.
Wet Single-Point Systems
A "Wet Single-Point" nitrous system introduces the fuel and nitrous together, causing the upper intake to become wet with fuel, usually in a spray-bar plate. However, the intake must be designed for wet flow (for example, carburetors also require a wet flow intake), as distribution problems or intake backfires may result. Dry-flow intakes are designed to contain only air, which will travel through smaller pipes and tighter turns with less pressure, whereas Wet-flow intakes are designed to contain a mixture of fuel and air. "Wet" nitrous systems tend to produce more power than "Dry" systems, but are correspondingly more expensive and difficult to install.
Wet Multi-Point Systems
A "Wet Multi-Point" nitrous system introduces nitrous and fuel directly into each intake port on the engine. These systems are also known as directport nitrous systems. Normally, these systems combine nitrous and fuel through several nozzles similar in design to a "Wet Single-Point" nozzle, which mixes and meters the nitrous and fuel delivered to each cylinder individually, allowing each cylinder's nitrous/fuel ratio to be adjusted without affecting the other cylinders. Note that there are still several ways to introduce nitrous via a direct port system. There are several different types of nozzles and placements ranging from fogger nozzles that require you to drill and tap your manifold, to specialty direct port efi nozzles that fit into your fuel injector ports along with your fuel injectors.