How was this magic smoke animation done?
If you want to do this from scratch you would need a software that has a particle simulation system. A popular tool for that is After Effects in conjunction with the plugin Particular from Red Giant. Its rather easy to use.

If you want even more realistic results you probably want to go with a more sophisticated solution often found in 3D packages like 3Ds Max, Cinema 4D or the the free and open source Blender.

If you dont want to render something yourself you can also buy stock-footage. A popular package is the Action Essentials 2 from Video Copilot. It offers pre-keyed (e.g. with transparency) footage from real smoke and fire and other misc. effects. You can easily colorize these to your liking and export them as a transparent png sequence.