Transparent background on the single particle and alpha blend mode for drawing.
This should be the most common method for general particles. The problem of this method is you have to sort the particles and rendering them back-to-front to get the alpha blending works correctly. It would bring a heavy burden on CPU when there is a lot of particles. And if the particles are not simple billboards and may intersect with each other, it may be unsolvable with simple sorting.
Black background on the single particle and additive mode as blending mode for drawing
You don't need to sort the particles, as the order of particles doesn't matter in additive blending. However, this method only works for a smaller set of effects, like fire.