Look, this is really really simple. (As a quick google of the subject will show.)
But first off, start with a good image. Facebook doesn’t “move the focus” or “wreck the exposure,” that’s the photographer.
Regular photos: 720px, 960px, 2048px (width)
Cover photos: 851px by 315px
If you use a 2048px photo, make sure to select the High Quality option when you upload it
To avoid compression when you upload your cover photo, make sure the file size is less than 100KB
Save your image as a JPEG with an sRGB color profile
There ya go, couldn’t be easier.