Quantum "teleportation" is a really strange phenomenon, but most popular-science descriptions fall a little flat, indeed.
Here's the basic setup for every quantum teleportation experiment:
- Two particles A and B are entangled and separated.
- Two more particles, A2 and B2, are put into two special states: A2 is put into some complicated wavefunction state, B2 is put into a "ground" state (a stable, predictable state).
- Particles A and A2 interact via some quantum dynamics.
- A and A2 are measured.
- The classical information extracted from this measurement is sent to B and B2.
- One of several quantum means-of-interaction is selected by the classical information, and then is applied to B and B2. So, they interact via classically-selected quantum dynamics.
- B2 is now in the state that A2 was put in during step 2. Some experiment is done on B2 to confirm this.
What happens to all of the extra information that is present in quantum mechanics but not in classical mechanics? The usual interpretation is that in step 4 above, a lot of it was instantly "transferred" to particle B, with the remaining information sent during step 5. However, that information from step 5 is crucially important to making the quantum information usable. Before you have that information, the difference is not detectable. So in some sense, no classical information gets transferred in step 4, and no quantum information gets transferred in step 5, but the combination is obviously transferred because the experiment in step 7 comes out the way you'd expect.
In general, entanglement cannot share information faster than light. This is because you can only notice entanglement when you take the two entangled systems and bring them back together, because entanglement manifests as strange, classical-probability-violating correlations between the two separated systems: and you can't observe the correlations until you have them both back together.
In the case of quantum teleportation, the classical information sent from the (A, A2) system to the (B, B2) system is not used to correlate two measurements but instead to transmit everything you need to reconstruct the quantum state over at B, which is often only a couple of classical bits. Still, it forms the same obvious barrier to transmitting classical information faster than light.