To my knowledge, this is implemented by making a square (based on your library it may be made using 2 triangles), applying a particle texture to it (I've attached an example one), apply billboarding, and then program something to make the rendered particle move and fade in/out.
Its noteworthy that there are in fact different types of billboards, for different effects. There are screen aligned BBs (as epicpunnum described), but there is even more of them:
Camera aligned billboards are nearly the same, but they are instead oriented towards the camera - try to visualize it, I'm too lazy to describe it right now :/
Then there are billboards that are aligned towards their own traveling direction. Think about sparks from an explosion - these do face the camera all the time, but the rotate around their own direction axis rather than the screen axis.
Last but not least, you might actually want to align billboards to a certain fixed direction sometimes. The shockwave of an explosion, or an old tree representation (âla SM 64) is such a case.
There was a good article which described how to achieve the different types of billboards using only cross products and a matrix as a local coordinate system. I have too little time right now to describe it for you, but if someone knows that article (or any similar), I think it would be great if he'd post this - that is definiately going to help with creating a good particle system.