Hit "Shift Return" whith the cursor in each line, to make it evaluate the line. (Or use "Evaluate Notebook" in the Evaluation menu to do them all at once)
Syntax matters - watch for square brackets vs curly brackets vs parentheses, capitals, colons, etc.

Here is a simple plot

Plot[Sin[x], {x, 0, 2*Pi}]

Here is an example where some control is exerted over the format of plot. See Plot in the documentation center for more options.

Plot[Sin[x],{x,0,2*Pi},AxesLabel->{"x value",f[x]},PlotRange->{-2,3},PlotStyle->{Dashed,Thick,Blue}]

Here is a static example of a sum of sine functions.

coef[n_] := 2 *(1-Cos[n* Pi])/(n* Pi)

vv[x_] := Sum[coef[n]*Sin[n * Pi * x],{n,1,20}]

Plot[vv[x],{x,0,2 Pi}]

What if you want to see what happens if the sum has a varying number of terms? You could just change the 20 and reapply but Mathematica provides a way to vary a term dynamically. Try this by moving the blue ball and then click the plus sign next to it and have it varied for you.

vva[x_,m_Integer] := Sum[coef[n]*Sin[n*Pi*x],{n,1,m}]

Manipulate[Plot[vva[x,m],{x,0,2*Pi}],{m,1,40, 1}]