How to describe the transformation that occurs in a function, and sketching the graph?

We use a method called H. S. R. V. with H = Horizontal , V = Vertical ,  R = Reflection , and V = Vertical movement.

X^3 is a graph that falls to the left and rises to the right.

"  -1  " at the end of X^3 means go down vertical 1 unit. So just shift the graph down 1 unit.

Yes, you plug in values of x and plot the result in the graph, then 'join' the values with a (curved) line.

Plugging in points always works, but calc will be easier if you know some basic shapes.
What you have here is a cubic function.  The PARENT function of this is y = x^3 which goes through the points (-2,-8)(-1,-1)(0,0)(1,1)(2,8)
Now you should learn that the negative in front of the x^3 turns this upside down and the -1 on the end slides the whole picture down one unit.  Or, you can just pick points.

The shape of a cubic function is like a snake.
An absolute value is shaped like a vee
A square root looks like an angel wing.  

Try something like this study guide from University of Wichita to help you
webs.wichita.edu/facsme/cbl/calculus/tofl.pdf
Once you know the basic shapes, you can make TRANSFORMATIONS on them with the other numbers and signs in the equation.