How to shoot such video?

I guess it depends... This was most likely done with simple compositing. If you are planning to do much video editing, then it is worthwhile to learn compositing, regardless of which app you choose. After Effects is probably the most widely used, so there is a lot of information on using After Effects. Vegas does compositing very well also, but lacks some of the refinements and bells and whistles that make After Effects so popular.

So if I was going to do a video like this, I would probably take both a video and a light painting still shot from the same angle, with 2 separate cameras. I would then overlay the still shot on the video clip, and use masks to reveal the light painting as it was being drawn, by altering the mask frame by frame. There are some shortcuts to make this easier (especially when you are elongating the mask linearly), but I would also expect this to take a bit of time to get it right...