A worksheet illustrating some of Mathematica's plotting capabilities.

We'll start by entering a couple of functions for later use.

f[x_] := x*Sin[x]

g[x_, y_] := x^2 - y^2

The most convenient way of plotting a function of one variable is the "Plot" command.

Plot[f[x], {x, -2, 2}]

If you want to look at a different part of the function, you can specify a plot of any domain you want.

Plot[f[x], {x, 0, 3*Pi}]

For plotting the graph of a function of two variables, use the "Plot3D" command.

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

It is sometimes also convenient to use a contour plot (which is called "ContourPlot"!)

ContourPlot[g[x, y], {x, -2, 2}, {y, -2, 2}]

If one is plotting experimental data you may need to plot list of points.  For this, use the "ListPlot" command.

Since we dont have a list handy,I'll generate one first.

L1 = Table[i^2*Sin[i], {i, 1, 10}]

ListPlot[L1]

If the dots are a bit smaller, you  can make them larger with one of the many "Options" that the various Plot commands admit.

ListPlot[L1, PlotStyle -> PointSize[0.03]]

Unless it is told otherwise, ListPlot assumes that the x-coordinates of the points in the list are 1,2,3,...  If you want the x-coordinates to be something other than the positive
integers you can just generate a list of pairs of numbers -- ListPlot will take the first number of each pair as the x-coordinate and the second as the y-coordinate.

L2 = Table[{i/4, i^2*Sin[i]}, {i, 1, 10}]

ListPlot[L2, PlotStyle -> PointSize[0.02]]