Rust is essentially oxidation, or a chemical interaction involving oxygen. When oxidation occurs in some elements, a thin film is formed as a result--such as the green layer that copper acquires. Other elements, such as iron, show rust as evidence of oxidation. If iron--or metal related to iron--is exposed to an environment both oxygen-rich and friendly toward the catalyst, then the oxidation process will begin. Molecules of iron at the surface of the iron object will exchange atoms with the oxygen in the air, and what atoms are left will form a new substance, the reddish-brown rust.
Air is not always necessary to cause rust, only the presence of oxygen, and oxygen can be found in water as well as air. In fact, water is usually considered the third part of the oxidation process, since it allows the oxygen and the iron to meet. This is why areas with lots of moisture in the air, with the presence of water vapor, have much faster rust rates than dry areas.
To look at it another way, oxidation is an electrochemical process that acts somewhat like a battery, exchanging small amounts of electricity. Like batteries, a solution helps this process by allowing electrons to move more easily between the two elements, and also like batteries, different solutions work better than others. Water takes some of the atoms and changes them into a light form of acid as the oxidation process continues, which helps metal rust even faster.
This acidic transformation occurs with pure water, but when the water is already salty it starts out as a minor acid and becomes an even more powerful electrolyte, facilitating the rusting process. There is then a hierarchy in the rust process. Rust does not easily form in dry climate, but in a wet climate the oxygen can access the metal more easily through the water vapor, and rust occurs much faster. Pure water forms an acidic solution and allows the oxidation process to happen more easily, and salty water works even better since it is already a catalyst. Prime rust conditions occur when the metal is regularly exposed to salt water and air.
For people who want to protect metal tools or vehicles against rust, there are a variety of waxes and oils that can be used to interrupt the oxidation process. Most of these work by not allowing water vapor to come in contact with the metal. Without water to help the elements exchange electrons, rust happens in barely noticeable amounts.