To understand how to model the climate it is important to understand how the climate works. The better we know how the climate works, the better we can model it.
Traditionally climate is defined as the average weather over a period of time, ranging from several to millions of years; the usual period is thirty years. Weather is the fluctuating state of the atmosphere around us. You may find it simpler to think of the difference as, ‘climate is what you expect; weather is what you get’.
When trying to describe weather we can consider breaking it down into weather elements like: temperature, precipitation, wind and clouds. Climate is the average weather and how it changes over time and between areas, for example, the climate in the tropics is very different from that at the poles. Statistically, relevant variations of the climate system occur only once in several decades or centuries making them easy to identify. However, weather is more variable and chaotic which means we are able to reliably predict it for only one week into the future, yet it is possible to predict global temperature changes for the next few decades.
The reason for our ability to predict temperature changes but not future weather lies in the fact that temperature basically depends on the energy balance (thermodynamics) of the climate system, whereas weather is a dynamic phenomenon. The thermodynamics of the climate system are quite well understood, but some important aspects of the dynamics are not, for example cloud formation.
The Earth’s climate is the climate of a complex, nonlinear system consisting of several smaller complex, nonlinear subsystems. The most important parts of this system are the atmosphere, the oceans, the biosphere, the lithosphere (the crust of the earth) and the cryosphere (the part of the earth that is permanently frozen). Every part of this system is in itself a complex system with distinct characteristic time scales ranging from days to millenia. Each subsystem is influenced by other subsystems and driven by what we call, external forcing. The basic driver of the climate system from outside the earth, the external forcing, is the incoming solar radiation.