AMD's "From vertex shader to mesh shader" [1] helps navigate between the older pipeline to the newer pipeline. Links in the sidebar get into other things like procedural geometry.
"Mesh Shaders and Meshlet Culling in Metal 3" [2] was also a good tutorial to learn about the mesh shading computation model.
I did most of my work in Metal. Apple WWDC's "Transform your geometry with Metal mesh shaders" [3] helped introduce it there. I liked playing with it in Swift -- this was a port of Apple's demos to Swift [4]. The Metal Shading Language manual also helps get your head around it. [5]