Since the aliens understand the same physics, mathematics, and chemistry as we do, we can use these to create a basic model of our world and build up from there. We can define our basic units of measurement- meter, second, kilogram, etc., using the fundamental properties of nature.
For example the second is based on the radioactive properties of the chemical cesium-133. And the meter is defined by the speed of light and the second.
"Qualitative" properties such as color, smell, etc., also derive from chemical properties. We could describe a certain shade of red purely in terms of its wavelength, or by its chemical properties. Smell again is purely a factor of the differing proportions of many different molecules in the air. I could describe the can of coke on my desk in nearly enough detail that they could reproduce it flawlessly: create a cylindrical shell of such-and-such aluminum compound of .1mm thickness. Fill it with 99.1% water, .2% sugar, etc. (again taking time to define what aluminum, water, and sugar are by their chemical components). Coat the aluminum shell with the following dyes, at these coordinates...
In this manner we could even get them to paint on the "Coca-Cola" logo and other designs. Now you may nod and say, yes, it seems that you can describe any such object with this precision. So the alien could create a world virtually indistinguishable for ours.
But not so. There is a fundamental property that we take for granted that is not so simple to communicate to the alien. And that is the property we know of left vs. right. To illustrate, look into a mirror. Imagine a world that looked exactly like the one in the mirror. How could make sure the alien was building your world, not the looking-glass world? To describe your world you must have defined a coordinate system, one with x,y, and z axis, all perpendicular to each other.
But even if the alien followed your instructions perfectly, he could still do so and end up with a different orientation, so that everything he did was reversed. Some curious properties would emerge in this world he created, but only relative to yours. The Coke can's writing would be reversed, but the alien wouldn't know. You might have said "make sure the 'o' is to the right of the 'C'". And the alien dutifully checked this, but if he used the reversed coordinate system, his left would be synonymous with your right. Not only that, but even the molecules would have reversed symmetry. While water would behave the same, your body would be unable to digest the sugar with "left-handedness"-- all your cells are designed to break down right-handed sugar. Is there no property of nature that would let you discriminate left and right before you arrived in the alien's world?
There are, in fact, some subatomic properties that have an inherent left/right orientation. One example is Beta decay. Richard Feynman describes how to define left/right using this phenomenon: "Listen, build yourself a magnet, and put the coils in, and put the current on, and then take some cobalt and lower the temperature. Arrange the experiment so the electrons go from the foot to the head, then the direction in which the current goes through the coils is the direction that goes in what we call the right and comes out on the left." "So, great," you think, "that saves me from going to a world where I'll starve to death and won't be able to read the Grey Labyrinth without a mirror. Kind of weird that it all hinges on such a non-obvious property."
But there's more. All the natural laws that exhibit this favoritism towards a particular left/right orientation are *reversed* for the case of their antiparticle. If you're not familiar with antimatter, antimatter is like "looking-glass matter". An anti-electron (more commonly called a "positron") has the same mass and physical properties as a regular electron, but with a positive charge. And an anti-proton is just like a regular proton but with a negative charge. So a positron will orbit a nucleus with an anti-neutron and an anti-proton just like an electron would orbit a regular nucleus. In this way, if the alien lived in an antimatter Universe, he would have built the mirror-image of your world and would not have noticed the reversal of left/right symmetry, because antimatter reverses all the natural laws which exhibit that property. Now if he did, you have a bigger problem to worry about than not being able to drink the soda. Anti-matter and matter are not compatible at a more fundamental level. When they meet, they cancel each other out and convert their total mass into energy via a process aptly termed "annihilation". A anti-Coke can weighing a little more than 12 ounces would react with 12 ounces of normal matter to produce explosion equivalent to thermonuclear bomb. As Feynman puts it: "... What would happen when, after much conversation back and forth, we each have taught the other to make space ships and we meet halfway in empty space? We have instructed each other on our traditions, and so forth, and the two of us come rushing out to shake hands.
Well, if he puts out his left hand, watch out!"