Spot, partial and centre weighted metering are essentially similar to each other, except the area of the frame which is metered is progressively larger. Basically each of these patterns will aim to record the metered part of the scene as a neutral tone (middle grey in black and white) unless you adjust the camera to do otherwise. If you aim the meter area at a generally pale target the camera will underexpose unless you dial in positive EC or, in manual mode, have the meter needle somewhere in the positive side of 0. If you aim the metered area at a dark subject/scene then the camera will try to brighten it to "middle grey" unless you dial in negative EC or, in manual, have the meter needle negative of zero. The behaviour of the camera is predictable and knowing how much +/-EC to dial in is a matter of experience and artistic or technical intent.
With evaluative metering things get way more complicated. Different cameras respond in different ways, but fundamentally the camera evaluates the entire scene and references a database to "guess" at the type of scenario you have. It biases the exposure depending on the active focus point, assumed to be on your subject, and possibly neighbouring focus points if they fall on equivalent tones (at a similar subject distance?). Often the outcome is quite decent, but it is hard for the photographer to predict how the camera will handle each scene and hard to know in advance how much EC might be needed.
I tend to use evaluative metering and hope for the best when shooting in Av and Tv modes, but for manual exposure, which I use most of the time, I use spot metering almost exclusively. I choose the area from which to meter very carefully and make a judgement about how bright it ought to be and set my exposure to place the meter needle where I think it should be. I may meter from something not even within the scene at all, such as my own palm, because I know how bright that should be. I also will often meter from the brightest important tones within the scene and set the meter in manual to +3, thus placing the brightest tones just short of clipping point in raw. This is classic ETTR technique. It puts me in charge of the exposure and not the camera and gives me the best raw file to work with in terms of the data contained within the file. It might not look right SOOC, but it will be the best starting point for raw conversion.