f=x^2+2 y^2-z
xmin=-5 ;xmax=5 ;
ymin=-5 ;ymax=5;
zmin=-5; zmax=5;
Gf=Grad[f,{x,y,z}] (* gradient of f *)
ContourPlot3D[f,{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]
cp=ContourPlot3D[f==0,{x,xmin,xmax},{y,ymin,ymax},{z,zmin,zmax}]
vp=VectorPlot3D[Gf,{x,xmin,xmax},{y,ymin,ymax},{z,ymin,zmax}]
Show[{cp,vp}]