Basic calculations require the use of *,^ for multiplication
and powers respectively. Thus, to calculate 5 times 2 raised to
the 3rd power plus 4 you would click in the expression below and
evaluate it by hitting [Shift]+[Enter]. 

5*2^3+4;

wxMaxima always uses exact calculations so sin(%pi) will evaluate
to 0 but sin(3) will not be simplified. Note that the symbols for
pi=3.14... and the Euler constant e=2.71... are %pi and %e.
Notice that when you type "(" the editor automatically enters ")"
so that you simply enter the expression between the parentheses.

sin(%pi);

sin(3);

In order to get a decimal approximation for sin(3),
enter float(%) in the input cell. Note that % refers to the
previously entered expression. Alternatively, you can use
decimal numbers such as 2.0 or 3.0 instead of 2 or 3.

float(%);

sin(3.0);

sqrt(2);

float(%);

sqrt(2.0);

wxMaxima can perform many algebraic operations. For example,
to expand the expression (a+b)^3 you would enter the
expression within the function "expand()".

expand((a+b)^3) - a^3;

When entering one expression divided by another you need to use
parentheses. Thus, 2x+1 divided by x^2+2 would be entered as 
follows: (2*x + 2)/(x^2 - 1). Its rational simplification can be
carried out by the function "ratsimp()".

(2*x+2)/(x^2-1);

ratsimp(%);

The factor and solve functions are very useful.
Just enter the expression within the function "factor()". Similarly
the solve function assumes the expression being equal to 0, and
it results in a list of all solutions for the variable x.

factor(x^2 + 3*x + 2);

solve(x^2 + 3*x + 2, x);

Lastly, one can correct any faulty input or change any previous
input statements and re-evalute the new expression as follows: 
- Select the expression by clicking it
- Edit the expression using the mouse and/or arrow keys
- Re-evaluate the new expression by pressing [Shift]+[Enter].