You don't actually have to do anything different in order to play games in the Fullscreen mode on one of your displays. However, having a game in Fullscreen mode means that your cursor won't be able to move from one monitor to the other while playing. This can actually be a good thing in shooters, otherwise you would click on things by mistake when your cursor switches from one monitor to the other.
It's also important to note that, visually, there's no difference between Fullscreen and Borderless Window. Both look the same, but the functionality is different.