KGeo supports three different operation modes. First of all there is the construction mode used to set up points, lines, circles and the like. Then there is the drag mode which allows you to drag around constructed objects, showing the immediate effect of this movement. For example let's think of the circle of Thales. If you move the point opposed to the hypotenuse of the triangle along the circumference of the enclosing circle, you will see that the angle remains a constant 90 degrees. The third mode is the trace mode. You can mark points, so that they leave a trace when they move, i.e. they leave a trace where ever they moved over and you can see the way an object went. Next I'll describe each of those modes in a more detailed way.
On the left side of the main view (canvas) you find all the tools needed to draw geometrical objects. The first button, for example, shows a point and that is exactly what is drawn on the canvas if you select this tool by clicking on the button and then clicking somewhere on the main view.
All the tools are organized in groups to help you to find the tool you are looking for. If you choose the segment tool, for example, you can click on two different coordinates of the main view and a line segment will be drawn between those two points. If you choose the segment tool a second time, you can also click on existing points and thus construct segments between points you have created earlier.
If you are not sure what a tool is doing just move the mouse cursor over the button and wait for a second. The tool tip will tell you exactly what you can do with it.