I know you are referring to making a classic combo video directly, but this really isn't the forum for this type of question.

In any event, here goes.

First you need skills. Make sure you know what you're doing when you're playing the game so that the combos are impressive enough that they are worth making a video for.

You need a source for recording your combos. Some kind of platform, like Playstation, N64, SNES, Genesis, MAME, an actualy arcade machine and a video camera, anything like that.

Then you need a method for recording. Something that record input from a source into your computer, of if you're using an emulator, some kind of on screen video capturing program like Camtasia.

After you record all your combos you will need some kind of video editing program. Camtasia comes with one, but I have never used it, I don't know it's limitations, but you should look into something like Adobe Premiere and/or After Effects. They cost a lot of money.

Anything else is going to be very specific, but that should get you started.