The problem with this is that is simply takes time.
The easiest way to start is to just mash the R button during any grapple or strike. Doing this, you'll probably do a reversal about 25-50% of the time. Not very accurate but it gets the job done to get started.
Every time you reverse a move, make sure you WATCH THE ANIMATION. In every move animation, there's a point where the animation will change into the reversal animation. You have to learn where these animation changes occur and get used to pressing R JUST BEFORE these happen. It's easier to get used to this if you're on a real console and have 2 people--you can just sit around and practice reversals all day.
Some other notes: You can counter the initial grapple animation by pressing L just before their arms touch you. Strikes work the same way, just press R right before their arm or leg touches you. It'll take some time to get the timing down. (Heh.)
You CANNOT counter weak A button grapples--scoop slam, wrist lock, knee to gut, etc.--because these moves actually RAISE the victim's spirit level! It's true. As such, they can't be countered because you would be losing the advantage it's giving you. (I suspect the reason it raises your spirit is because most of the weak A button grapple moves tend to put the victim in a position where it's very easy to put on a submission move.) So if you see someone doing one of these, don't even try to reverse it, it's a waste of time.
Other than that, I can't give you much advice.