There are several things to work out. If you have an actual character, not just a camera, then parent the character's hand to the gun and rotate/position the gun so that is looks like the character is holding it when he is animated. Then, when the character starts moving, the gun will go wherever his hand goes. If you can't see the gun, then move the hands up into view because realistically a human moves there arms into there view not their head into their arms. :)

If you don't have a character model, then you only have to parent the camera to the gun and move the gun into a position in front of the camera where you can see it.