As has been pointed out, it's impossible to use an entangled pair to send any information. To elaborate a little, the point is that you can only make one measurement, and a single measurement tells you very little about a state. For example, if you measure the spin of an electron to be up, then you only know that it's not in the spin down eigenstate. On the other hand, if you do a bunch of repeated measurements on electrons all prepared in the same state, and get spin up every time, it's a good bet the state is at least approximately equal to the spin up eigenstate.
Turning back to the original scenario, let's say two particle are entangled so that they have opposite spins: if one is up, the other is down. These are sent off to obserers A and B. Then A will try to send a message to B, say an answer to a yes or no question, by the following scheme:
1. If he wants to send yes, he should measure the electron, collapsing its state.
2. If he wants to send no, he should not measure it, leaving it in a superposition.
Now if B measures his electron, let's say he finds it to be spin up. What does this mean? Well, either A wanted to send yes, and measured his electron to be spin down, or he wanted to send no, and B was the one who collapsed the state. These are equally likely, so there's no way for B to know what A did, and so no information is sent.
On the other hand, let's say B could copy the state of his electron into the states of many other electrons (ie, so that all the electrons have the same state as the original), and measure all of their spins. If he found them all to be spin up (or all spin down), he'd be reasonably sure A collapsed the state, and so wanted to send yes. If the distribution is 50/50 spin up and spin down, he'd know the state was not collapsed, and so the message is no.
Thus if it was possible to copy states, it would be possible to send information faster than light. Luckily, there's a theorem called the http://en.wikipedia.org/wiki/No_cloning_theorem" which says it's not possible to copy states in this way. The proof of this uses simple linear algebra. It's interesting that such a simple, and seemingly unrelated, mathematical property of quantum mechanics is crucial to the consistency of quantum mechanics with special relativity.