Needs["VectorFieldPlots`"];
f[x_,y_]:=(x^2+4 y^2) Exp[1-x^2-y^2];

Plot3D[f[x,y],{x,-2,2},{y,-2,2}]

ContourPlot[f[x,y],{x,-2,2},{y,-2,2},ContourShading->None]

Manipulate[Show[GradientFieldPlot[f[x,y],{x,-a,a},{y,-a,a}],ContourPlot[f[x,y],{x,-a,a},{y,-a,a},ContourShading->None]],{a,0.1,2}]

g[x_,y_,z_]:=(x^2)+(y^2)-(z^2);
Show[GradientFieldPlot3D[g[x,y,z],{x,-1,1},{y,-1,1},{z,-1,1},VectorHeads->True],ContourPlot3D[g[x,y,z],{x,-1,1},{y,-1,1},{z,-1,1}]]