Let us assume that transportation of human beings (and other objects) is possible (maybe in the future), and we have the technology to do so. (Please don't debate the scientific plausibility of this.)
Every atom can be copied (one-at-a-time) in its exist chemical state and relative position, from one point in space to another. Meaning that the copied human has the exact chemical composition right to the sub-atomic level. The entire process is too fast for a significant change in structure to occur during the process.
Here are 3 ways of doing this:
Physical displacement - Every atom is physically displaced via some kind of passage.
Wormholes - Every atom passes through a wormhole, and is instantly repositioned at the location.
Creation of matter - Every particle is scanned and destroyed to form energy. This energy is taken to the site and converted back into matter, in the exact same state as earlier.
Will this being have the same 'sense of self' as us? Will we now continue to inhabit this body, or will we be destroyed, and the clone will have its own sense of self? Note that every memory and thought in the brain will be transferred in the same chemical state.