Well, that depends. Most people I know just use Adobe After Effect to create any sort of animated visuals. Or you make them at runtime with some tricks, methods and shaders/effects. If After Effect or baking them at runtime is beyond you - there are also software that do that and only that, such as TimelineFX, Magic Particles or Particle Illusion but they all are rather limited in use and scope.
I would advice you to just learn After Effect. Specially as it can be used for many things, not just VFX.