Upon start, you will be presented with an empty working space, or canvas. (If you already drawn a molecule and want to start anew, choose the menu File > New or click on the
button)
In the beginning, all atoms you add will be carbons; don't worry, it is better to change them into another element once you have them drawn.
If the molecule contains rings, it is generally better to start with them.
Use the templates provided in the toolbar:
click on one of the buttons ,
then click on the canvas, once for each ring;
when you are done, click on the button.
To draw rings with a single common atom, when you are positioning the second ring click on one of the atoms in the first ring (it will be highlighted).
To draw condensed rings, when you are positioning the second ring click on one of the bonds in the first ring (both affected atoms will be highlighted).
Then, draw the chains, one bond at a time: click on button (if not already selected) and then on the atom where you want the new atom to be linked. To bond two existing atoms, click on the first one and, without releasing the mouse button, drag to the second atom.
To convert a single bond into double or triple, click on the single bond using the tool. You can also use and to add stereochemical information to an existing bond.
To modify the chemical element of an existing atom, click on one of the buttons etc. and then click on the atom(s) whose identity you want to change.
If you need other elements, you may use the periodic table
Edition
Positioning the mouse pointer over each button in the toolbars* you will see a floating tooltip with its function.
(* in the JCP panel, not here)
Drawing or moving:
With the drawing mode is activated, adding bonds.
You can move (translate) atoms by dragging them once they are selected.
Selecting atoms:
You can select a single atom by clicking on or and then clicking on the atom. If an atom was selected previously, you must deselct it by clicking on the empty canvas, then you can select the new one.
To select a group of atoms, click on and draw a lasso line that surrounds the desired atoms, or click on and draw a rectangle that surrounds the desired atoms.
Remove atoms:
To delete an atom, click on it after choosing the tool.
To delete several atoms, select them with or and then click on any of them with .
Undo actions:
To undo the last action, click on . (May be used successively.)
,
button.
and 
to add stereochemical information to an existing bond.
etc. and then click on the atom(s) whose identity you want to change. 
or 
and then clicking on the atom. If an atom was selected previously, you must deselct it by clicking on the empty canvas, then you can select the new one. 
tool.
. (May be used successively.)
.