Understanding your meter
Okay, so you can get a long way by just trusting your meter, using your histogram display to adjust exposure and using bracketing if you need extra reassurance. To get beyond a certain level, though, you need to understand how to use your meter to get a good exposure first time. By knowing what your meter is trying to do, you can either accept its recommendation or deliberately increase or decrease exposure in situations where you know this won't give the best result. By practising dialling in exposure compensation without taking your eye off the bird in your viewfinder, you can make sure you get a correctly exposed shot no matter how fleetingly the opportunity appears. (Well, most of the time!)
So what does your meter try to do? Simplistically, it tries to make your image mid-toned on average, so that if your picture contains nothing but mid-tones (e.g. a field of grass on an overcast day), it would come out at the correct exposure level. If the scene contains a wider range of tones (e.g. the same field of grass under bright, backlit sunlight), the meter tries to set the average of these tones to mid-grey, so that they will have the best chance of all being captured without over- or under-exposure.
I say simplistically because modern multi-segment meters (when set to matrix or evaluative mode) take many separate readings from different parts of the image and apply advanced computing and pattern-matching to au[/tomatically compensate for extremes of brightness in a range of image types.
Applying exposure compensation
In practice, the effect of this sophistication of modern meters is to reduce the amount of exposure compensation needed. You will, therefore, see a difference between my guidance and that based on the use of older average or centre-weighted-average meters. You will normally need to compensate in the same direction, but with a reduced amount. In the following image captions, I'll describe the compensation that should be used in various scenarios. It’s worth taking the time to study how the histograms relate to the image in each case. A summary table is included at the end.