The Plot3D function is the main way to plot a 2-variable function:

Plot3D[ Cos[x] * Sin[y], {x,-2*Pi,2*Pi}, {y,-2*Pi, 2*Pi} ]

The ContourPlot function plots level curves. In its simplest form, Mathematica chooses a selection of curves to plot.

ContourPlot[ x^2 - y^2, {x,-3,3},{y,-3,3} ]

The Contours option lets you choose the contours to plot:

ContourPlot[ x^2 - y^2, {x,-3,3}, {y,-3,3}, Contours->{-1,0,1} ]

The ContourPlot3D function, given an expression rather than a full equation, is an extension of ContourPlot to plot “level surfaces” for 3-variable functions.

ContourPlot3D[ x^2 - y^2 + 3z^2, {x,-5,5}, {y,-5,5}, {z,-5,5} ]