An example of how to do splines. You can use them for everything, from simple drawing (vector images, here we come) to control paths of sprites or particles and even making music.
<img src="http://dl.dropbox.com/u/11182740/pictures/splines.png" border="0">
Press 'esc' for a help screen explaining the use of the mouse and various keys.
I didn't comment it, but will try to answer specific questions, if posted here.
A spline is defined by nodes. The connection between two nodes is called a segment. Every node has two controls. Control a (the red dot) controls the curve leading to that node. Control b (the green dot) controls the curve leaving that node. That means, every segment is influenced by two controls, control b of the starting node and control a of the ending node.