When you press down the right stick to counter the attack, do you just press it, repeatedly press it, or press and hold?
The counter knife is a quick time event. You need to press the button at the right time. Repeatedly pressing it should work too, as I have countered when panicking with a button spam. I don't believe there is a penalty for hitting the button too early, purely based on my experience with the game.
You don't need to hold the button down. Possibly out of habit you may hold it down during the animation, but it is not needed.
I've been knifed a few times from the front and each time I try to counter I fail.
The window is small. If you fail it is most likely because the timing was off. Sometimes you may be victim to some lag, which falls into the category of "how did I die if I shot you first?". There really isn't much you can do about this other than playing on servers local to your region.
As you have mentioned, you need to see the attacker. You cannot counter a knife attack when it comes from behind. You should see the prompt on screen to counter the knife.
Perhaps your thumb stick is damaged (slightly) meaning you need to be a little more forceful with the press. I have had this occur on controllers in the past.
It isn't uncommon to have a string of failed counters. Once you get used to the mechanic you should see more success. From my experience, a lot of knife attacks are actually surprise attacks (coming from the side or behind). I only started becoming more successful at countering when I stopped panicking. As soon as I seen the knife animation start or someone lung at me from the side I would instinctively hit the counter button.
There are plenty of youtube video guides on countering. I didn't find any useful other than understanding that you cannot counter attacks from behind.
Also, if you believe you are about to be knifed and hold down the right stick until you are knifed, will that counter an attack, or do you have to press it down just at the right time?
Yes, you need to press it at the right time. You can't hold the button down beforehand. The button press must be done within the specific time frame.
@CommandoAir added a useful comment as follows:
It's also important to note that counter-knifing is very bugged. It rarely actually works and you rarely get the on-screen prompt. I don't know if it's down to lag or something, but unless they are directly in front of you the game seems to count it as a knife from behind.
As you can see, the mechanic does cause problems for other players, so much so that it is described as bugged or broken.
Best Answer
You (or your victim) only gets a chance to counter the knife attack if you try it head on (you and your victim are facing each other).
To guarantee a kill without a counter, you have to attack from an angle (from the side, from behind, etc.).
The "magic punch" in the video happens because the opportunity to counter was missed, and not due to a specific button combination.