Why Heisenberg Is Right (and wrong)
Heisenberg's theory claims you can't measure a particle down the tiniest detail, it will be somewhat inaccurate. However, to transport a particle you will need to know the exact details and then produce another particle with those same characteristics somewhere else. Correct? Well, not really.
The basic foundation to Quantum Teleportation is the concept of entanglement. In this process, two photons are "entangled" (would make sense, right?). Two entangled photons act like any others, until a measurement is taken.
Measure the polarization of a photon (being part of a light wave), and it is vertical or horizontal. (Actually, there is no absolute "vertical", there are only two states perpendicular to each other). A photon has a 50% chance of being in either state. If you set up a polarizing filter (like those in polarized sun glasses), it would let in 50% of a light wave through, those photons with a polarization the same as what the filter lets through.
What's so special with entanglement? Simple, once photon is measured to be either vertical or horizontal, the other will be measured to the exact same way. (As if when rolling two separate dice, the roll of one always matches the other.) Each measurement by itself will always be a 50% chance, only the two measurements will happen to match. Sound weird? Einstein called it "spooky action at a distance."
Now the real questions: When can I be teleported? How much will it cost? Can I have the schematics to build one and be rich? Now the answers: Not anytime soon. Nothing more than photons has been transferred.
If you take some unknown photon (say, photon X) and have it interfere with one of the entangled pair (say, photon A; the other is going to photon B), the result could behave in a certain set of ways. The particles could cancel, reenforce, or could have been polarized different ways and do nothing. However, the effect of this mess can be applied to photon B (by rotating the polarization) and making a perfect copy of photon X (without ever finding out what it really is).
At the University of Innsbruck, they really did this. However, they only transferred a quarter of the photons (only those when X matched A). Since they controlled the polarization of X, they could make sure it was really being teleported.
Another interesting effect arises from this: entanglement itself can be teleported. A can be entangled with B, and the new copy would still be entangled with B. Weird.
No-cloning (nothing to do with Dolly the sheep)
You can't make an exact copy of a particle. Sorry, no-can-do. If did, you could get around Heisenberg's theory (by measuring one accurately for position, the other accurately for momentum; together, you detailed information for both, unlike what Heisenberg said). Unfortunately, nature likes the rule and prevents you from copying it, you can only move it.