What metering mode you choose to use can depend on the overall scene lighting, and also can factor in your Exposure mode.
Evaluative metering does a scene "average" with an "emphasis" on the center of your focus. It can be fine if you are fine with a medium average exposure, like when you are shooting in the Program mode, Tv or Av mode and don't want to bother with "fiddling" and, especially, if your scene doesn't have any dark shadows or bright highlights.
Be aware, though, that a huge part of the "craft" of photography is developing the abiloty to "judge" the light, both in a scene and by checking your results and making adjustments when necessary. This can be important with Evaluative metering (and any mode, in fact). After taking a shot and checking your review with the histogram turned on, you have to learn to spot when things are off. At that point you will need to apply Exposure Compensation (in P, Av and Tv modes) or, if in Manual, to make adjustments to your aperture, shutter speed or ISO to correct things. In the non-Manual modes, you have to remember something important: if you will need to focus and recompose, then that will normally throw your metering off and you will need to prevent your exposure from being thrown off by activating Exposure Lock -- check your manual for the "how to".
Each of your other metering modes (Partial, Spot and Center-Weighted) are different ways of metering a part of the scene so you can accurately evaluate the lighting involved and respond to that evaluation by making adjustments. Again, you can use any of the Exposure modes, just remember the different approaches required for Exposure Compensation and Exposure Locking.
And, something that was mentioned above is that these "partial/spot/center" modes can be very useful when you are trying to set an exposure that is, say, darker or lighter than "medium" -- you set your exposure or Exposure Compensation to the "proper" interpretation of the subject, so that if it's bright, you might set your exposure/compensation so that the meter needle goes to maybe +2 Ev or, if the subject is dark, set the needle to, say, -2 Ev.
Or, of course, the subject may actually be one that you want to be "medium" but perhaps there is either a lot of shadow or maybe bright reflecting lights that could throw your exposure off -- you could set your camera to ensure that the subject gets a "medium" exposure.
A simple illustration of the basics of all this is to use the example of Manual exposure and Spot metering. These two settings work "hand in glove" to illustrate what I've been talking about, and what you learn can be applied to the other modes as long as you understand what is happening and what you are doing and why.
First, one of my favorites in practice is when I'm shooting on a sunny day with a bright blue sky. In those conditions I really try to shoot with the sun somewhere behind me so it doesn't interfere with my lighting so much...
So you have your camera set to Manual Exposure and your metering to Spot. Your exposure settings can if you wish be at some derivative of the "Sunny 16 Rule" (Aperture f/16, ISO 100, shutter speed 1/ISO or 1/100, or a derivative by moving one setting for whatever reason and the others to compensate). Of course, a derivative setting would take into consideration things like movement and depth of field. For this exercise, though, "ballpark" is a good place to start.
Now, you could stop at the Sunny 16 settings, and if it really is a bright sunshiney day you would be fine. But for a couple reasons I won't stop there: first, I have found that the actual lighting conditions often don't "match" the Sunny 16 settings. Second, it's good to have your own "standard" so you can always double-check your settings. And third, this little exercise would be useless if we just settled for Sunny 16.
So, here's what I do: I get as much of the blue sky as I can in my field of view, especially at the middle of it, and I activate the meter (half-press of the shutter button) and then check the metering needle. Now from experience and learning I know that a nice blue sky will be "somewhere around +1 Ev. Maybe a little more maybe a little less, but certainly for the initial shot(s) +1 Ev is a good place to set the meter needle -- you either adjust your shutter speed, aperture or ISO to set the needle there (for this stuff do please turn off any Auto ISO setting).
Once you do this, in Manual your exposure is not locked. You can then focus on another part of the scene and take a shot. Because the scene as a whole shares the same light, each shot will have a decent exposure and a consistent exposure. Of course if the lighting changes or you turn and shoot in some dark shadows, then it's time for a recalculation.
Now, rather than assume I'm all done, I will typically take the time for one more consideration, and that is highlights that may risk being blown. A good quick way of doing this is to find the brightest spot in the scene (a bright white cloud is a good example) -- shoot it and check the review for highlight clipping. If they are there, you may want to dial back the exposure until they go away. But, if the brightest part of your scene that has any meaning to you does not clip, you can brighten things a bit (especially if you are shooting Raw).
And then, if you have dark shadows, that's another concern -- you may considering notching up the exposure if those shadows are pressed against the left of the histogram.
Well, that was quick and easy! If you "get it" you can apply the same learnings in various ways. Here in POTN, one favored approach is to use the palm of your had as the "measuring stick". To do this properly, of course, your palm needs to have a "known" value which depends on things like skin tone. So, to get this accurate you can take a medium gray card and hold it up in the scene lighting and (in Manual) get the meter marker centered on the gray card. Because you are in Manual, your exposure settings will stay locked, so if you take the card away and then stretch out your hand with the palm facing the camera, again in the "normal" scene lighting, you will see the meter marker move -- it will be showing how your palm differes in brightness from the "medium". This becomes a reference for your future shooting. For example, if your palm shows up at +1 Ev, well then you will know that for a shot if you have a scene with "normal" lighting (something around daytime lighting) you can use your palm to set your exposure -- +1 Ev on your palm will render a good exposure on your scene, assuming you do the needed little checks I talked about above. Of course, if the scene has bad lighting you will want to reconsider your calculations, but then that's all part of the craft. And, another nice thing about this is it doesn't depend on a bright blue sunny sky like my approach does
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Now note that we used Spot metering here. Actually, for the blue sky spot metering may not matter so much, but it may for the hand. It's your judgement call -- you read the descriptions of the partial metering modes in the manual, maybe do some internet reading, and make an informed choice as to what portion of the scene you want to use to meter and set the exposure. And, remember -- if you don't shoot in Manual Exposure mode, that's OK, you can do the same thing -- meter on something with a "known" value, adjust your Exposure Compensation to set the marker at that level, and then enact Exposure Lock before you recompose and focus on something else.
You can, though focus and recompose if the part of the scene you are metering has something you can focus on without losing your exposure, but that can be tricky. In Manual though, you have locked your exposure so you can focus/recompose or recompose/focus freely.
So, as far as the different modes, I hope you can see where Spot, Partial and Center Weighted can play a different role -- use spot if you have a spot or narrow area that you want to ensure that you "get it right", partial and Center take in a bigger area, either one that has one big tone or one that you want to "average out" to a given exposure -- this can happen when a critical part of your scene needs to be "correctly" exposed and you don't want to be thrown off by other parts of your scene that are lighter or darker, but for this instance Spot may not really nail it.
And, for one fun exercise: imaging a bride and a groom on their wedding day, posing for shots outside in some nice light at their reception. The bride is in a bright white wedding dress while the groom is wearing your standard black tux.
So, you are the photog -- what Exposure settings do you use? What metering mode would be best?
Well, it's up to you. You could start with using the Evaluative metering mode and a semi-auto exposure mode -- P, Tv and Av. Shoot, check your results, hit Exposure Compensation (and Exposure Lock), shoot, check, adjust, and repeat until you get it right. And, there is nothing wrong with that, we've all done it before and will do it again, because it's a quick approach that doesn't require much thought beforehand, and as long as you know what you are doing and get it right, then fine!
But, just drawing on what we've talked about, you can get to a superior "starting point"!
Remember that brights can be dialed up to +2 Ev and darks to -2 Ev? Well that applies here except that the real data can go farther. In fact, a pure white can be dialed up to +3 Ev without clipping and the scene will retain detail, but that is indeed pushing it, and you will get highlight "blinkies" unless you set your Picture Style to Neutral and your Contrast setting all the way back to -4. But, the important thing to digest here is that if you get a good exposure on the bride's dress (or on the black tux) you can get a great "starting point" exposure without all the test/adjust/reshoot hassle.
This is a scenario where Spot metering can really come into its own -- spot meter on the bride's dress and adjust your exposure to where the dress is exposed to either +2 Ev (which will be up against the edge of the scale) or, if you wnat to "go there" up it another notch or two -- +2 1/3 or +2 2/3 can do fine, even though the marker will be off the scale and unless you did the Neutral/-4 Contrast settings your highlight blinkies willbe going nuts. But, when you bring the shot into your computer, that dang dress will be nice and white, and you will have plenty to work with in the less-than-bright parts of the scene, including detail in the black tux!
Of course, you can follow the same approach with the black tux -- setting the black to a negative Ev setting without pushing against the left side of the histogram will ensure that there is detail in the black, wereas if you were to do an automatic exposure and maybe use Evaluative metering it is likely that either the black will be underexposed with the Evaluative or, if you let the camera meter off the black and then Auto Expose, the camera will expose to try to push the black to Medium, giving you a nice light tux, but then look at the bride's dress and you'll want to hide your eyes
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Well, I hope that all helps a bit!