How exactly is it done, which Street Fighter games feature it and how quickly do I have to do it in order to cancel after a Shoryuken into a forward dash Metsu Hadouken?
you can cancel a normal attack into a special move by performing the special move before the animation for the normal has completed. for example, a standing hard punch cancelled into a hadoken.
to cancel a shoryuken into a dash then metsu hado isn’t a normal cancel. it’s a FADC aka Focus Attack Dash Cancel. To do that, after the first hit of the shoryu you need to hit focus, then dash forward, then perform the metsu hado. FADCing requires 2 ex bars.
It takes some practice though of course, first start off just canceling your Shoryuken with an FADC dash forward until it comes naturally to you, then start practicing the Ultra, its how I got it down, it really helps.