Just off the top of my head,
A) follow assiduously the rules of firearms handling
There are several different versions, but they assert the same principles
here is one site http://thefiringline.com/Misc/safetyrules.html
Here is my personal version:
RULE I: Treat all firearms as if they are loaded and capable of sending a bullet out the muzzle. Unless they are disassembled or with the action open and personally checked by you with no interruption in possession or attention.
RULE II: Never let the gun point at anything you are not willing to put a bullet through, destroy or kill. I recognize that all guns are pointed somewhere
ALL THE TIME. Be aware of where (and what) that is, ALL THE TIME. If you ask yourself what the muzzle pointed at during your handling and you cannot answer, you are not paying attention well enough. -OK, that may be extreme, but you get the idea, I hope.
RULE III: Keep your finger off the trigger until the gun is pointed/aimed at an object you intend to put a bullet into.
RULE IV: Be sure of your intended target and what is beyond it before pinting the gun (or pulling the trigger, especially).
My version is a bit more complex than most, but that is just my style.
B) Before doing anything, announce your intention and ask permission to do what you intend to do. The respect shown to the store will earn you the respect of the store.
C) If you are not INTIMATELY and CERTAINLY familiar with the operation of a firearm, ask for a store employee to show you the operation of dis-assembly. It would be polite if you asked even if you know the operation and/or dis-assembly. After all, the clerk does not know what you know and will respect you more if you ask.
D) When handling any firearm and pointing it to check the pointability, sight picture, etc., be particularly observant of where you are pointing it. I usually pick a corner of the room significantly ABOVE the heads of any visible people.
(edit #2) Or, better yet, as Theohazard does, ask the store to recommend an aiming point.
E) Mechanical risks to the firearm (perceived or real, no matter) Do not open or close any revolver action unless you do it gently (such can bend the crane). Do not let any semi-auto close on an empty chamber under full return (recoil) spring power (a round in the chamber cushions the impact). Do not dry fire any firearm unless the store says it is OK (dry firing some actions can damage the mechanism (or may be perceived to put the mechanism at risk) or may appear to violate firearms handling rule #1. If you have personally verified that the firearm is empty and the store is OK with it, go ahead and dry fire. If not, don't.
Even if the store says dry firing is OK, I usually put my thumb or a piece of wood (pencil, popscicle stick or something similar in front of the hammer to absorb the impact. This allows me to feel the trigger/sear release without steel-on-steel impact where (when firing actual ammunition) it is usually steel on brass or mild steel (less shock)
Almost EVERYONE knows not to do the "wrist flip" closure of a swing-open revolver. Fewer consider that the same crane-bending forces apply when opening a revolver.
I was in a gun store and brought my revolver in because I was interested in getting some new grips for it. I offered it (in a hardshell case and with no grips installed) to the clerk to verify it was unloaded. He picked it up, pressed hard on the side of the cylinder with two fingers and released the cylinder release, flipping the cylinder open with a GREAT deal of force.
I was aghast.
I will NEVER let that clerk handle another of my firearms again, under any circumstances. And I am a forgiving person.
Do not give any gun store reason to distrust your gun handling skills or knowledge as that clerk gave to me. (Note: This particular gun store is one of the most respected in my town, and I regard the staff as highly knowledgeable in gun handling and loading. The departure from proper gun etiquette surprised the heck out of me.)
That you ask how to properly conduct yourself speak volumes about your maturity, earnestness and respect for firearms and your fellow man. Kudos to you, sir. You have my respect and best wishes.
edit: I started composing this post before any of the other posts arrived. Sorry if I repeated any of the prior advice.