An easy one (if I remember correctly) if you want to try with an akuma and jill valentine (akuma currently fighting, jill "next in line"). Bear with me, I haven't played the game since the arcade.
1. courching light kick-> crouching medium kick (I believe those are the same button) -> hard hurricane kick as akuma (if you can't get this combo, then you'll need lots and lots of practice for harder ones)
2. while in air and falling from hurricane kick, fireball + both punches to have akuma do air super combo (lots of air fireballs)
3. As opponent is falling from those and about to hit ground, fireball + both kicks (I think) will bring out jill and have her do the tyrant super combo.
So, just a lot of stuff like that was in the video along with lots of dashes, etc. etc. Just takes practice and maybe reading some combos on gamefaqs or a MvC2 site.