Cloth evaluation aside, a more basic question is how does one know this was “Our Lady of Guadalupe”?
The story and the resulting good fruit are very compelling. While, generally speaking, the Church accepts this event as miraculous, and while Pope Benedict XIV pronounced Our Lady of Guadalupe as the patron saint of Mexico, no Catholic is obligated to believe in this miraculous event.
But I do.
Cloth evaluation aside, a more basic question is how does one know this was Our Lady of Guadalupe?
The short answer is that it has been carefully guarded (but not preserved since 1531). Many Native Americans have touched the cloth before it was put under control probably about 200 years ago. It is a miracle in itself that this piece of cactus cloth did not disentegrate from the handling over about 200 years... But miracles occurred because of the image, and that is why it has been carefully guarded since December, 1531...
Since you ask the question, there are two. Long before the miraculous appearance on the tilma in Mexico City, there was a statue of Our Lady of Guadalupe in Spain.
In fact, after Cortez conquered Montezuma and his people (in Mexico City), when Cortez returned to Spain, he spent 9 days in front of the statue in Spain (Our Lady of Guadalupe in Spain).
Of course, there was no Mexico City in existence when Cortez conquered the Aztecs. It was their city with pyramids and altars for human sacrifice...
The image (Our Lady of Guadalupe [Mexico City]))had a special meaning to the Native Americans. When the miraculous event occurred, runners when from village to village drawing the image. It was understood by the images, as the image of Our Lady of Guadalupe (Mexico City) has special things that Native Americans understood.
For example, the BLACK QUARTER MOON that the woman is standing on is one of the Native Americans gods.
The fact that the woman is bowing to a higher being meant to the Native Americans that they worshipped a false god.
One way to know is that the original was painted over by the Native American Indians to make her look more like them...
There are a number of certified miracles associated with the original image of Our Lady of Guadalupe (Mexico City) -- an Indian was killed by accident by some celebrations regarding the image (being shot by an arrow). The person was brought before the image and came back to life.
The other occurred in the 1920s when the FREE MASONS tried to blow up the image, but even with powerful explosives, they did not even crack the glass (it was not protected by bullet proof glass back then)...