We just put in a whole house fan. It does a few things.
It pulls air throughout the house and exhausts it through the attic. This means that you get a few benefits. First, it cycles air in your house quickly, so if the temperature outside is cooler than inside, it quickly cools your house. Second, because it vents to the attic, your attic air temperature decreases much more quickly than it naturally would, because you are forcing all the warmer air inside the attic out.
Regarding box fans, you need to realize that a box fan itself isn't going to be as efficient as its rated CFM without modifications similar to what
@YttriumNitrate is suggesting in order to actually keep the fan blowing air in the right direction. You can't really create negative pressure from a fan that has a large area immediately by the fan that is letting air back into the house.
In any of these setups you need to be wary of pulling in humid air, as it's not difficult to pull in "cool" but super humid air and cause moisture problems.