Final cut pro x, editing

Im not positive, but I think you can do this with any software. I think you just take out little parts of the video, like not even a second long.

Yeah it's this. Pretty simple to do.

Just find the video clip you want to do it to, then just start making .5-1 sec cuts every second or so.

Yeah thats just skipping frames. The best way to do it is to turn on audio waveforms so you can see where the audio peaks are, and use the blade tool to make cuts at each of the beats where you want it to skip frames. Then take each piece and drag both the beginning and end forward a few frames, so at each cut it jumps forward a bit. Then just tweak it until it looks good and flows with the song you are using.

In fcp x you would click b to activate the blade tool, cut the clip at the desired beat then use the trim tool (click T) to cut a little bit away from the next clip.