One of the many things that draws folks to the great outdoors here in the southwest is the remains of ancient Native American cultures like the Hohokam around Phoenix and Tucson, the Salado in the Supes, the Sinagua up around the Verde Valley and Flagstaff, and the Anasazi and Mogollon along the Colorado Plateau country. It is a wonderful experience to encounter these ruins out in the wild, without fences, gates, signs, or trailmarkers. However, for this experience to continue, its important that people visiting the ruins act with respect - otherwise, it would be all to easy for the land managers to declare areas off-limits. While there is no one "proper way" to act while visiting ruins - each person has their own way of approaching them - some basic rules should be followed.
Leave it where it is
One of the biggest problems facing archeological sites, especially those in the backcountry, is the removal of artifacts. It is always a joy to walk into a site and find potsherd littered across the ground, like a form of pavement. They're still there for you to see because most people who've visited have left things where they found them. Do the same. Potsherds, corn cobs, stone tools and flakes, and especially bone should never be moved from their original resting position. Taking a piece of pottery and moving it even to another area of the ruin and dropping it will ruin its scientific value to any future archeologists. Some people will say that you shouldn't even pick up artifacts to look at them, but I believe that as long as they are placed back in the exact spot they came from, there's no harm done. The exception is bone - especially if its human. Touching a bone can "contaminate" it. If an anthropologist wants to study the genetic heritage of that person, and you touched their bone, it renders the test unusable - leave bones alone!
Don't pick up pieces of pottery, corn cobs, or building stones and place them on walls or boulders. It's rude, because it robs the next person of the thrill of discovery, and as I said above, it destroys the scientific value of the piece.
If you see a nice piece of pottery coming out of the ground, don't try and dig or pull it out. Pulling can break it, and digging (even something small) in a ruin without a permit on federal land is a crime.
Don't walk through the midden
The midden is the trash pile, usually located in front of a cliff dwelling. On surface sites, it can be harder to detect. The midden is usually where the residents burried their dead, and tossed away their broken pottery. However, it is also very soft, and walking across it can disturb the soil, churning up the relics. Archeologists rely on the midden layers to determine the sequence of occupation of a site, as well as help estimate diet and population size. Unless there is already a footpath across the midden, don't walk across it. If there's no other way to get to the ruin - don't go in. Observe from a distance.
Don't eat or go to the bathroom in the ruin
This one is a no-brainer. Eatting creates crumbs and detritus that attracts rodents and other animals which can nest and burrow in the ruins, causing damage. And urine and feces obviously aren't helpful to preservation, let alone being unpleasant to the next visitor.
Don't lean on the walls
Also pretty obvious, you don't want to lean, push, pull, or stand on ancient walls or structures. They're ruins, you know, and your attention may be the last little bit that it needs to send that perfect kiva roof colapsing.
This is the hardest one for many people, but its usually not a good idea to bring your dog into a ruin. You may know not to jump on walls, or pee on pictographs, but your dog doesn't. They've also been known to start digging into the ground in a ruin. The same reason you shouldn't dig in a ruin also applies to your dog. Tie them to a tree nearby with some shade and water and explore the ruin without your canine friend.
Archeologists use carbon-14 dating (along with tree-ring dating) to determine how long a site was occupied, and at what times. Burning anything in a ruin can mess up the data, telling the archeologists that the site was built in 2006, and abandoned the same year. Never build a fire in an alcove unless its a life-or-death situation. Archeological sites in alcoves may not be easily visible.
Camp at a distance
Along the same lines as the above, make sure that if you're backbacking into an area known for ruins that you don't camp in them. They may seem like good campsites - ready made walls and a roof, but there's often lots of rat droppings, which can have hantavirus, and possibly valley fever in the room dust. You don't want to get to close to all that with your face for several hours of sleep.
Don't touch the rock art
Rock art, both painted (pictographs) and pecked (petroglyphs) are fragile, and easily affected by the oils in your hand. View them at a distance or close-up, but don't touch or chalk them (sometimes done in the past to make them stand out). Some people like to make rubbings or tracings of petroglyphs, but this is also harmful, as it can erode the sides of the image faster than what would be natural - sketch or photograph them instead.
Wow! Lots of guidelines for something that has no one specific "right way." With this set of guidelines and a good dose of common sense and respect for the ruins, you should be in good shape for an ancient encounter, whether its your first or hundred-and-first time seeing the past.
Remember always to check with the local land management agency, as some areas have specific rules regarding certain sites or areas. As always, remember how it looked when you first got to the site - try to leave it just the same for the next people.