Simply move the sliders around, and try the check boxes. Amplitude controls the lobe sizes. Phase controls lobe orientations. Spiro gangs the x and y amplitude and frequency controls, and sets the phases for symmetric spirographs. Decay makes the curve spiral inwards.
Color sets a black background, and draws the picture in color.
Thick draws a thick line. This also slows the drawing speed. Leave the phases alone for true spirographs. You can change them for interesting effects, but the pictures won't then generally be spirographs. After conducting several searches, I believe this applet is unique in being the only one that makes it easy to draw spirographs and Lissajous figures, as special cases of harmonograms.