I am trying to get an intuition of what a metric is. I understand the metric tensor has many functions and is fundamental to Relativity. I can understand the meaning of the flat space Minkowski metric ημν, but gμν isn't clear to me. The Minkowski metric has a trace -1,1,1,1 with the rest being zero but how do I "find" what the metric is in General Relativity? I know that the metric is spatially dependent and locally flat, but how exactly does it depend on spacetime? I heard sources say that the metric is simply given or stated for the type of curved coordinates that you happen to be working in. From the metric derivatives you can get the Christoffels, from the derivatives of the Christoffels you can get the Riemann and from the Riemann you can get he Ricci curvature...etc. but how do you get the metric to begin with? I know its related to the Newtonian potential for the 00 components 1/2g00⇒Φ I am sort of lost when it comes to understanding the other components.