Hit "Evaluate" to see the results of each computation. You can edit the contents of a cell to do your own computations.
You can do arithmetic.
You can multiply out.
You can factor.
You can (try to) solve equations, and use show() to ask for pretty formatting.
Here is an example of plotting. You can use sin(x), cos(x), log(x), exp(x), etc. Powers are done as x^2 or x**2. Use parentheses and * for multiplication. The second argument is the interval to plot over.
Here is one that is discontinuous at 0. Try zooming in by changing the interval to (-0.1,0.1) etc.
You can plot piecewise defined functions. (At the breakpoints f evaluates to the average of its two sides, which is not usually what you want.) By default, only the results of the last command are printed; if you want more, then explicitly say to print them.