ThreeDimensional Surface Plots
Plot3D[f,{x,x_{min},x_{max}},{y,y_{min},y_{max}}] 
 make a threedimensional plot of f as a function of the variables x and y 
Basic 3D plotting function.
This makes a threedimensional plot of the function sin (xy).
Out[1]=  

Threedimensional graphics can be rotated in place by dragging the mouse inside of the graphic. Dragging inside of the graphic causes the graphic to tumble in a direction that follows the mouse, and dragging around the borders of the graphic causes the graphic to spin in the plane of the screen. Dragging the graphic while holding down the
Shift key causes the graphic to pan. Use the
Ctrl key (
Cmd key on Macintosh) to zoom.
There are many options for threedimensional plots in
Mathematica. Some are discussed here; others are described in
"The Structure of Graphics and Sound".
The first set of options for threedimensional plots is largely analogous to those provided in the twodimensional case.
  
Axes  True  whether to include axes 
AxesLabel  None  labels to be put on the axes: zlabel specifies a label for the z axis, {xlabel, ylabel, zlabel} for all axes 
BaseStyle  {}  the default style to use for the plot 
Boxed  True  whether to draw a threedimensional box around the surface 
FaceGrids  None  how to draw grids on faces of the bounding box; All draws a grid on every face 
LabelStyle  {}  style specification for labels 
Lighting  Automatic  simulated light sources to use 
Mesh  Automatic  whether an xy mesh should be drawn on the surface 
PlotRange  {Full,Full,Automatic}  the range of z or other values to include 
SphericalRegion  False  whether to make the circumscribing sphere fit in final display area 
ViewAngle  All  angle of the field of view 
ViewCenter  {1,1,1}/2  point to display at the center 
ViewPoint  {1.3,2.4,2}  the point in space from which to look at the surface 
ViewVector  Automatic  position and direction of a simulated camera 
ViewVertical  {0,0,1}  direction to make vertical 
BoundaryStyle  Automatic  how to draw boundary lines for surfaces 
ClippingStyle  Automatic  how to draw clipped parts of surfaces 
ColorFunction  Automatic  how to determine the color of the surfaces 
Filling  None  filling under each surface 
FillingStyle  Opacity[.5]  style to use for filling 
PlotPoints  25  the number of points in each direction at which to sample the function; {n_{x}, n_{y}} specifies different numbers in the x and y directions 
PlotStyle  Automatic  graphics directives for the style of each surface 
Some options for Plot3D. The first set can also be used in Show.
This redraws the previous plot with options changed. With this setting for PlotRange, only the part of the surface in the range 0.5≤z≤0.5 is shown.
Out[2]=  

When you make the original plot, you can choose to sample more points. Mathematica adaptively samples the plot, adding points for large variations, but occasionally you may still need to specify a greater number of points.
Out[4]=  

Here is the same plot, with labels for the axes, and grids added to each face.
Out[5]=  

Probably the single most important issue in plotting a threedimensional surface is specifying where you want to look at the surface from. The
ViewPoint option for
Plot3D and
Show allows you to specify the point
{x, y, z} in space from which you view a surface. The details of how the coordinates for this point are defined are discussed in
"Coordinate Systems for ThreeDimensional Graphics". When rotating a graphic using the mouse, you are adjusting the
ViewPoint value.
Here is a surface, viewed from the default view point {1.3, 2.4, 2}. This view point is chosen to be "generic", so that visually confusing coincidental alignments between different parts of your object are unlikely.
Out[6]=  

This redraws the picture, with the view point directly in front. Notice the perspective effect that makes the back of the box look much smaller than the front.
Out[7]=  

The ViewPoint option also accepts various symbolic values which represent common viewpoints.
Out[8]=  

{1.3,2.4,2}  default view point 
Front  in front, along the negative y direction 
Back  in back, along the positive y direction 
Above  above, along the positive z direction 
Below  below, along the negative z direction 
Left  left, along the negative x direction 
Right  right, along the positive x direction 
Typical choices for the ViewPoint option.
The human visual system is not particularly good at understanding complicated mathematical surfaces. As a result, you need to generate pictures that contain as many clues as possible about the form of the surface.
View points slightly above the surface usually work best. It is generally a good idea to keep the view point close enough to the surface that there is some perspective effect. Having a box explicitly drawn around the surface is helpful in recognizing the orientation of the surface.
Here is a plot with the default settings for surface rendering options.
Out[9]=  

This shows the surface without the mesh drawn. It is usually much harder to see the form of the surface if the mesh is not there.
Out[10]=  

To add an extra element of realism to threedimensional graphics,
Mathematica by default colors threedimensional surfaces using a simulated lighting model. In the default case,
Mathematica assumes that there are four point light sources plus ambient lighting shining on the object.
"Lighting and Surface Properties" describes how you can set up other light sources, and how you can specify the reflection properties of an object.
Lighting can also be specified using a string which represents a collection of lighting properties. For example, the option setting
Lighting>"Neutral" uses a set of white lights, and so can be faithfully reproduced on a black and white output device such as a printer.
Out[52]=  