Color is a very large topic indeed. Anything I say on the topic is likely to be very partial. can not be separated as an issue from any of the other subjects on this page, indeed it is the means by which many of them are effected. In the consideration of color, separate attention should be paid to the lightness, saturation and hue of the image. Lightness and saturation are both ramp values (between zero and one) and the these two values within a painting often look the same when they are mapped.
Interesting results can be had when they are clearly different, as below. This is particularly useful when making landscapes.
Hue is a different animal: it is a thing of variety not quantity. It is a famously difficult thing to get a grasp of, made more difficult by the fact that it is tied in subtle perception-driven ways to saturation and lightness. One 'handle' you on hue you should develop is a knowledge of hue's place on the hue wheel. Oposites on the wheel are also perceptually opposite and this opposition can be used within a painting.
In the painting below by Thomas Moran yellow and purple (oposites on the wheel) 'drive' the look of the painting.
However, near neighbors can also oppose. In the image below the 'lemon yellow' of the lemon and the 'cadmium yellow' of the flower are clearly different.
But arranging hue is not a simple case of pairing two hue values of similar saturation and lightness value. It is an immensely complex thing that is not bound by any one understanding. It is significant that the many people who have written on the topic of color harmony are very rarely in agrement with each other. It is best learned by example, and the best exemplar is the work of painters: