Souinds like this is your first rifle. Or at least your first lever rifle. Not a very good action to start out with only because of the safety aspect. I would bet that your Henry Long Ranger has a transfer block system. If you're not aware of this what it does is the transfer bar does not allow the hammer to strike the firing pin unless the trigger is pulled fully rearward. For hunting you carry the rifle with a round in the chamber and the hammer DOWN!
Should you cock the hammer with a round in the chamber and you decide not to fire you simply hold the hammer and pull the trigger and allow the hammer to move slightly forward. You can then release the trigger and the hammer will continue to lower to its "rest" position under the control of your thumb. But should the hammer slip from your thumb and the trigger is not pulled the rifle SHOULD NOT fire. However as bocojnala stated you must ALWAYS keep your muzzle pointed in a safe direction.