one or two eyes??

I practice with both eyes, but it takes a while to train your eyes to focus on your dominant eye if you're not accustomed to it. I was just looking into this a few days ago for handguns. I have a really hard time focusing on the sights on my handgun unless I briefly squint with my left eye. The guy in this video says that's normal, at least at first. I think similar logic applies to scopes. I find that if I close one eye, my eyes get tired. If I practice using both eyes, my brain gets tired. Pick your poison I guess.

 
I'm a one eyed shooter for pistols and rifles. I shoot shotgun with both eyes open though. With a shotgun I know that I'm shooting where I'm looking, I don't need to look at the sights. I know it sounds silly, but I shoot a lot of trap this way and I'm pretty darn good at it. With a pistol or rifle, I need to see the sights and I have a hard time focusing on the sights. I would like to open the other eye but, I need a lot more practice at it.
 
I have always shot with both eyes open. It comes from hunting [moving] rabbits with my .22LR when I was a kid. You needed to have both open to track with one eye (the left in my case), and shoot with the other. You do not close either eye. Rather you "switch" your brain from one eye to the other. The left eye (no scope) guides your aim to the rabbit. Once you see the rabbit image flash into the scope (right eye), you hit the switch to the right, and go from there.

I tried shooting with an eye closed just to see what it was like. It was very uncomfortable and left me with temporary blurry vision in the closed eye. If, for whatever reason, I had to shoot with one eye closed, I think I would prefer to wear a patch.




 
I prefer two eyes opened. The only "problem" is that sometimes my brain stop working and mess with my focus. When this happens I just close my eyes or look to anything else and restart the process.

I use both eyes opened for open sights and for scopes.

​I read somewhere that you have more light with both eyes and consequently a better vision of the target.
 
Two. In weapons training they teach both open. Helps to also spot what else is around and or if a non combatant walks/ flies into the danger zone or you pan into a potential bad shot, like a window, that you might otherwise not see since the scope is focused on the target and everything else around it is either out of sight or out of focus. 
 
I prefer both eyes open, but after a long time of not shooting I find that I now need to retrain my brain to easily focus on my scope eye. 
Like ztirffritz said, it takes some practice to shoot with both eyes open. 

But there is no right or wrong about one or two eyes, it comes down to personal preference and how you shoot: target, hunting, etc. 
 
I use both eyes open for three reasons. Situational awareness, Less eye strain and I use a scope level when bench resting that is in the field of view of my left (non scope) eye. Takes some training but I can see the level well enough even though its out of focus with both eyes looking at the target. In other words I'm not trying to focus each eye on something different. Its easy once I got used to it. 
 
Interesting question and one I have to think about to tell you what I do. I keep both eyes open. I am very left handed and very left eye dominate. It really doesn't matter what my right eye does. I suspect people who have issues with this are those that are right handed and LH dominate (or vise versa). Just guessing here as I can't relate. Just speculation after thinking about it. If I were right handed, shooting right handed, and left eye dominate I am sure my left eye would be trying to get in on the action. The natural way to overcome this would be to shut my left eye. I have taught a number of young kids to shoot guns and bows. And they first thing I do is figure out which is their dominate eye. You would be amazed how many people are cross eye dominate. In these cases I teach them to shoot right or left handed based off which eye is dominate. Since these are kids it's a little easier since they don't know any better.