Sword etiquette is a simple subject which is based on three things: basic knowledge of the Japanese sword, good manners, and common sense.
There are a few things to remember in regards to knowledge. The first and foremost is to never touch the sword blade with bare hands. The sword should always be held and or handled by the nakago only. Do not speak while holding the sword, even the tiniest drop of spittle can cause rust to a valuable piece of art. If you have questions, ask them after returning the sword.
When viewing the sword, it is permissible to use a provided soft cloth to lay the blade on. The cloth is opened and spread across the palm of one hand, then while holding the nakago in the other hand, the upper portion of the blade is placed on the cloth. Many times there will be a piece of paper placed inside the cloth, if so, it is unfolded along with the cloth and the upper portion of the blade is laid on the paper. The sword is ideally viewed under a single-point light source in front of and slightly above your head.
Good manners are simply that. Be polite and courteous to the group or owner of the sword(s) you are viewing, as well as all others present. Ask permission prior to picking up a sword or any item which does not belong to you. Say "Thank you" when you are done.
Now for common sense. Most of these things should be no-brainers:
Pick up a sword without asking permission.
Touch the sword with your hands or fingers.
Wear lots of bling (necklaces, bracelets, jewelry) that could hit or scratch the swords.
Have cameras, purses, or anything else hanging or dangling from your person.
Swing the sword around, practice kata, or turn away from the table where you are standing (others may be in close proximity).
JAPANESE SWORD SOCIETY OF HAWAII 2011