Control points are added by left-clicking on the canvas. Left-clicking also has another function: moving existing control points. Basically, if you click within five pixels of an existing control point then you grab that control point rather than add a new control point. So, if you want to move an existing control point left-click on it and drag it to its new location.
When a control point is added to the canvas it will be displayed as a white point, and the curves will be updated to include the new control point. No curves will be displayed until a minimum of two control points have been added: then, the Bezier and Hermite curves will be displayed. The B-Spline curve requires three points for display; the Cardinal spline requires a minimum of four points for it to be displayed. Note that the B-Spline curve is identical to the Bezier curve if there are only three control points (this is due to the way I have implemented B-Spline curves with evenly spaced knot points).
The Hermite curve is displayed in yellow. The Bezier curve is displayed in green. The B-Spline is displayed in blue, and the Cardinal spline is displayed in red. Note that my Cardinal spline is actually a Catmull-Rom spline, because the tension is set to 1/2.
If the Hermite curve is being displayed then the control points will include the tangent vectors (in yellow) for the Hermite curve. The tangent vectors are displayed as yellow lines radiating from the control point. The direction and magnitude of the tangent can be changed by grabbing the tip of the tangent vector in a manner similar to the way control points are moved - by left-clicking within 5 pixels of the tip of the tangent vector. The Hermite curve will be updated in real-time as the tanget vector is modified. Note that the right-hand tangent vector in any pair of control points (except for the last control point of the curve) is displayed with its direction reversed (the vector is reflected about the y-axis). This is to prevent it from overlapping the left-hand vector of the next pair of points. (See Foley, van Dam, et al Computer Graphics: Principles and Practice figure 11.16 (section 11.2.1) for more information on why this is a good thing.)
The "Clear Control Points" button will remove all control points (and therefore all curves) from the display, and in effect reset the applet to its starting condition. The various checkboxes (Display Control Points, Display Bezier Curve, etc) control what is displayed. Each checkbox controls whether a given feature is displayed or not. The Increment scrollbar controls the step size used in the curve calculation loop: a larger increment (moving the scrollbar slider further to the right) means that the curve will be displayed in a coarser fashion (fewer line segments will be used to approximate the curve).