There is a built-in plot theme:
(*First@*)Plot3D[x^2 + y^2, {x, -2, 2}, {y, -2, 2}, PlotTheme -> "Detailed"]
Uncomment the First@ if you want to remove the plot legend.
First@
Here is a start
Plot3D[ x^2 + y^2, {x, -2, 2}, {y, -2, 2}, Boxed -> False, FaceGrids -> {{0, 0, -1}, {-1, 0, 0}, {0, 1, 0}}, FaceGridsStyle -> Directive[Thick, Black, Dotted], PlotRangePadding -> None, AxesStyle -> Thick]
