2. ALWAYS CHECK THE WEAPON to see if it is loaded. Even if you just saw someone else check the weapon, even if you know it's unloaded, ALWAYS visually inspect the weapon before handling it further. This means opening it up to check any places where a live round might be. Do this WHENEVER you pick up the weapon -- someone reaches under the counter in a weapon store to show you a weapon -- check it. For semi-automatics, remove the magazine, work the action to eject the round in the chamber, then stick your little finger into the barrel forward of the chamber to make sure it is clear. Then look through the barrel from the chamber toward the front of the weapon, if there is enough light to ensure that it's clear. You hand someone an unloaded weapon to hold while you shift some ammo cases. When they hand it back -- check it. It should be a routine matter of habit, anytime you pick up a weapon or someone hands you one.
Never accept into your possession a weapon that you do not know how to check! Ask someone to show you how to check the weapon first. Don't fiddle with it thinking you'll figure it out.
3. ALWAYS keep the weapon pointed in a safe direction. If you are at a range, keep it pointed downrange. When reloading, be aware of where the weapon is pointing. It should be pointing at the target, or into the ground. If your weapon is holstered, your holster should direct the muzzle downward at a relatively acute angle, not poking out from under your arm to endanger everyone standing behind you. If you are hunting, keep your rifles pointing skyward if slung, or into the ground if carried, not aimed at the butt of our your friend in front of you. Don't lean on a rifle. Don't cowboy-twirl your single-action revolvers. Etc.
When cleaning or repairing a weapon this might not be possible -- it's difficult, for instance, to keep the weapon safely pointed while looking down the barrel. When cleaning, either the action is open and the ammo has been removed or the weapon has been disassembled.. Be cautious, and use common sense.
4. Unless your weapon is ON THE TARGET, keep your FINGER OFF THE TRIGGER. Simple: on target equals on trigger, off target equals off trigger. Easy to say, but the trigger is a natural place to rest a finger when holding a weapon. Don't do it! Keep your trigger finger straight, resting against the side of the trigger guard. The only time the finger comes to the trigger is when the weapon has been brought to bear on the target you intend to shoot.
Once you know this rule, you can watch nearly any weapon-handling TV show or movie to see how commonly it is violated. If you are a TV cop approaching a possibly lethal situation, your weapon should be at ready, pointed in a safe direction, finger OFF the trigger. Carrying the weapon, examining the weapon, drawing the weapon from a holster--whatever. Finger off the trigger until the weapon is on the target.
5. The oft-repeated, NEVER point your weapon at anything you are not prepared to shoot. This doesn't mean that if you have pointed a weapon at something that you are obliged to pull the trigger. It DOES mean that anything you point your weapon at could possibly take a bullet, whether you intend it to or not. It also means you NEVER brandish your weapon or threaten anyone with it unless you are in an immediate life or death situation and you are prepared to use it. It means that it doesn't matter if the weapon is loaded or not--handle it as if it were.
This rule, again, is ridiculously ignored in movies. People are always gesturing to each other with their weapons. Watch the arc that the muzzle covers when they do this. People who cross your body while waving their weapons around are not your friends.
6. Be sure of your target and what is beyond it. This means NEVER point or fire at anything that (1) you cannot clearly and unambiguously identify as a target, and (2) that would pose a danger to anyone were your bullet to stray, ricochet, or over penetrate. It means always knowing where your bullet has the potential to go. Never point the weapon or pull the trigger at a close-range target without a backstop that will STOP your fire. Dry firing? The weapon is unloaded, eh? SEE RULE #2. Only fire against a backstop. There are too many results to this rule to list, especially when it comes to open-range target plinking, long-distance shooting, and self-defense situations. Using safety ammo is supposed to reduce over penetration of the target, but it won't keep you from hitting a bystander if you miss. Be sure of your target.
7. Store and transport your weapons safely. There is no strong consensus as to what constitutes safe storage and transportation, so it's up to your discretion. Some people keep all their weapons in a fireproof basement weapon vault with their ammunition stored separately, other people keep their hand weapon loaded and on their person at all times. Investigate the options, and exercise your common sense. You should know that if a child ever acquires a firearm due to your negligence, you could be federally liable. Be aware that your vehicle typically stands a much greater chance of being burglarized than your home. Factory ammunition doesn't constitute a fire hazard, but be careful where you store it. Investigate the options, make a formal determination about how your weapons will be safely stored and transported, and then stick to it.
A couple common rules of thumb are: never be separated from a loaded weapon -- if the weapon is away from your person, in your car, at home alone, etc, it should be unloaded. And never depend on hiding a weapon to keep it from a child.
8. Shoot with eye and ear protection. Simple, eh? Obviously in some cases (self-defense, hunting) you may not be able to, but you'll be better off when you do.
9. The common-sense rule of threat avoidance: never do anything when you are armed that you wouldn't do if you weren't--i.e., intervening in a robbery, going outside your house to investigate noises, going to tell your drunken neighbor to shut up, etc. Think about leaving the weapon behind. If you wouldn't do it without a weapon--DON'T DO IT. Call the police, swallow your pride, take the loss -- whatever. Don't carry a weapon into a potential conflict where you feel you might need it. Avoid the situation. Simple advice, but sometimes difficult to follow. Don't be macho, be smart.
10. The tenth and final rule--never hand a weapon to anyone that doesn't understand and abide by these rules. Once they are holding the weapon, it is their, not your, responsibility to handle it safely, but you have your conscience to live with.
These are just the basics. If you do things like hand loading, hunting, skeet shooting, practical shooting, or open range plinking there will be a pile of other safety considerations. You should know federal laws, and the laws in your state. Keep these rules in mind, and you may well live to be a happy handler of many weapons.