By quantum entanglement
. Absolutely do not try this, people will look at you funny.
Until recently, it was thought that quantum entanglement offered the best chance of transmitting information faster than light. it's kinda true but not in any useful sense. Here's the idea: you take two particles, and entangle them. Now, there's a coupla ways you could do this but creating them both simultaneously from energy so that they're each other's antiparticles will do it nicely. The idea here is that if two objects are entangled, changing the properties of one affects the properties of the other because the universe has to balance its books so that all the time antiparticles have opposite spin or whatever. So, you tangle the particles, move one to Alpha Centauri 4.3 light-years hence, and keep one here. As they are quantum entities, they exist in both states simultaneously (in a probabilistic sense - according to the Copenhagen interpretation this is also a real sense) until the state is measured, at which point they 'collapse' into one or the other.
Ok, so you've got a particle here and a particle there, and you measure the state of one. Now, if the probability wave collapses (ignore that phrase - it just means the particle ends up in one state or another) into one state, and the other particle must always posses the opposite state, then the other particle collapses instantaneously into the other state. As in, faster than light can take the information there. I don't want to think about what general relativity and its effect on simultaneity does to this idea, maybe later, but there's a very good reason you can't use this for communication or 'information transfer'.
You're not transmitting information. The people in Alpha Centauri can measure their particle, but that doesn't help much with regard to information. The information is not the state itself, but some concept surrounding the state - ie the role the state plays in some prearranged code. As you cannot control what state the waveform collapses into, you can't use it in a code. Simple eh?
The observers at either end can, in other words, know the state of the particle at the other end, but they can't communicate via this knowledge.
It has been suggested that you could force the waveform to collapse, and thus use a sort of morse-code arrangement to send info via quantum entanglement. My fault for not making it clearer when I was making the node - the receivers have no way of knowing if the wavefunction was collapsed before they looked at it to see if it was collapsed. When they look to see if it is, it collapses and they have no way of knowing if they did it or if the senders did. No butter came