Modern SLR cameras usually have up to 4 different metering modes to choose from.
Each mode measures the environment differently, and because of this, only certain modes are suitable for some situations.
Centre-weighted: You'll find this mode on just about any modern camera.
It's quite an inaccurate method of measurement because it's quite old and was designed around the technology of the time.
Technology has advanced quite a lot since this method of measurement was invented, which is why we have other modes available to us these days.
Centre weighted metering references the levels of brightness in only the middle of the frame.
The cameras computer then calculates an average across that area, and then uses that value across the whole frame.
It's really not useful in situations where the brightness of the scene varies across the frame.
Spot metering: Spot is quite the opposite with differing brightness levels.
Spot can provide excellent results in these types of scenes.
A very small area in the centre of the frame is measured - as little as 4%, and that specific value is then applied across the frame.
You should always use AE Lock (Exposure Lock) with this mode, and note that it takes some experience to know where to take the measurement.
To use spot-metering, set your metering mode to spot mode, identify the area in the frame that you wish to measure and arrange the frame so the exact centre is pointing at this spot.
Lock in the measurement by pressing the "AE Lock" button.
Measurement done, now you're ready to compose and take the shot.
Partial metering: Partial mode is specific to the Canon EOS range of cameras.
The method of measurement and usage is basically the same as spot, but there is a difference.
The size of the area used to take the measurement with partial is about 10% or so.
Matrix metering, or Evaluative metering: Matrix mode is the default for most cameras.
It's quite a complex method of measurement, and it's very clever, because it takes many readings is different places across the frame.
It then suggests a reading based on an average which has been calculated based on all of the measurement points.
Experimentation is always the best teacher, but I will offer a little guidance here.
Spot or partial modes are especially useful for environments with very dynamic or contrasting lighting conditions such as a rock concert or theatre.
Other metering types can be confused by the dark background.
When taking a measurement, aim at the performer to lock it in, then shoot away.
Matrix-mode will most likely be suitable for just about everything else, but don't be afraid to experiment.