We characterize and classify the quantum states of a pair of spin-½ particles in terms of the entanglement of the pair. We describe a general strategy for classifying the quantum states of entangled systems, and apply it to the simplest entangled system available - a pair of spin-½ particles. The method is based on local unitary transformations. We give a set of six parameters that describe an arbitrary pure state of a pair of spins, one of which is the entanglement of the pair. We discuss visual representations of the state of this system, and propose a visualization using a Bloch sphere for each subsystem and a disc to record the `shared' information.