A hybrid is one way to do it.
The basic principle is that the line carries both incoming and outgoing signals at the same time but you mathematically (as done with a hybrid transformer) subtract your known outgoing (transmit) signal from the total and the remainder must be the signal from the other end. In practise, some of the outgoing signal from the microphone is also fed to the earpeice (sidetone) to prevent the human reaction of shouting if you can't hear yourself!
Most modern telephones don't use hybrid transformers, they do the subtraction using op-amps.
Brian.