Use your mouse to click and drag to draw on the applets. You may draw on either grid. As you draw on one grid you will see the corresponding image under the map in the other grid.
For example, if you draw on the left grid you will see the conformal map of your drawing appear on the right grid... and conversely, if you draw on the right grid you will see the inverse conformal map of your drawing appear on the left grid.
You may select the thickness of the line you draw by choosing the pixel size of your stroke in the "Line Width" pull-down box. Similarily, you may choose the color of your lines with the "Color" pull-down box.
There are "Reset" and "Undo" buttons for your convenience. Reset clears everything that you have drawn, while undo erases the previous paths you stroked, one at a time.
The orange dots on both grids represent equivalent units. These allow you to compare the scales of the grids.