Evaluative metering.
Your focusing screen is divided into numerous little invisible portions rather like a honeycomb, and each portion is metered individually. The camera then analyses the scene and compares it with thousands of sample images stored on board to try to arrive at the ideal overall exposure for the scene based on all those readings. Nikon's system is very similar except they call it Matrix instead of Evaluative. Individual manufactures are very cagey about the information they release on these systems and the nature of the stored sample images, but that's the bare bones of it.
Evaluative, whilst it can be fooled by extreme lighting conditions, is pretty reliable in most circumstances.
Partial Metering
Just meters from one area of the screen, usually a zone around the centre of the screen (but larger than a spot metering area.)
This is useful when you want to meter for a particular tone in your shot, ignoring darker or brighter areas. A good example would be a head and shoulders portrait taken with a bright background such as the sky, where the partial zone would meter from the skin tones of the subject while ignoring the brighter background.
EDIT
Sorry I ddn't see you asked about spot metering.
True spot metering is best done with a good hand held meter, and the narrower the angle of the spot reading the better. Better hand held meters read a 1 degree spot angle for taking accurate readings from very small areas.
Spot meters in cameras read from a larger angle - usually around 6- 9 degrees, so still very useful for metering from a small tone in your scene when you're trying to decide the best overall exposure for the scene.The camera spot metering area is usually marked with a circle in the centre of the focusing screen.
To get the best from spot metering you really need to have a pretty good grasp of basic exposure principles or you can cause more problems with it than you solve. For example if you tried spot metering on a magpie, you have only two tones .....black and white, so you'd end up with gross over or under exposure depending on whether you metered on a white or black bit of the bird - It's a classic situation where an 18% grey reading would probably give the best result.