Lightmeters in modern (digital) cameras are intelligent enough to automatically determine the correct exposure for most shots so the photographer can concentrate on composing the image. They all work on the principle of measuring reflected light from the subject. The three most common types are discussed here.
Center-weighted metering asesses the whole image area but assigns the most importance to the central 40 to 60%. This system is accurate in average lighting conditions, but can be fooled by excessively dark or light areas.
Spot metering only evaluates a small area in the center of the viewfinder so you can meter for a specific detail of the scene (e.g. when photographing a subject against a bright or dark background).
Matrix-metering divides the image area into many small segments and analyses the readings for the best possible exposure. It is remarkably accurate in most situations.
Automatic exposure modes work fine for most scenes, but the meter can only see scenes as neutral gray and compensates for any deviations accordingly. So you should know when to override the meter's results. If the subject contains more than average dark or light tones you should take a substitute reading of an average gray area, lock that exposure and then recompose the image and release the shutter.
Green grass or medium blue sky are good examples of average gray.