You can move a control point by dragging it with the mouse, add a new one by clicking the mouse, and delete one by holding down the Shift key while clicking on it.
Controls 0123 define a cubic curve going from 1 to 2. Controls 1234 define a curve going from 2 to 3 and so on The tangent to both curves at 2 is parallel to the line joining 1 to 3.
Unlike a natural cubic spline, a Catmull-Rom spline has local control. This means that modifying one control point only affects the part of the curve near that control point.