Brad,
Mac is right about the real safety, however there is a safety feature built into current production guns that is better known as the "transfer bar". This transfer bar only moves into a position to strike the firing pin when the gun is cocked and will remain up to strike the firing pin when the trigger is pulled and held back. If you cock the hammer it's ready. If you want to let the hammer down without firing, (MAKE SURE THE MUZZLE IS POINTED IN A SAFE DIRECTION) plant your thumb firmly on the hammer spur holding it back then depress the trigger momentarily only enough to allow the hammer under your thumb to start traveling forward slightly, then release the trigger and slowly allow the hammer to return to the uncocked forward position. The transfer bar will move down and out of the way of the firing pin as long as you are no longer holding the trigger and if it is working as it is supposed to be. If you were to be cocking your gun and your thumb happened to slip off the hammer half way back a gun without the transfer bar would likely be accidentially discharged by you, with the transfer bar it would not provided it is working as it should because the transfer bar would move down out of the way as the hammer is falling provided your finger is NOT on the trigger. This feature also prevents a bumped hammer from the rear from striking the firing pin since the transfer bar is down and out of the way. The H&R/NEF guns do not have a hammer block safety or trigger block safety. All my transfer bars work as they should and is one of the first things I test when I pick up one of these guns after making sure the gun is unloaded and pointed in a safe direction.
The transfer bar is also used in late model Ruger revolvers if you are more familiar with those.
The best safety when using any gun is as Mac says, right between your ears. I think they are one of the safest guns out there, either they are cocked or uncocked with no mechanical safety to fail.
Hope that helps.