Nerve cells communicate in a region called the synapse. Here, in response to an electrical impulse, one nerve cell releases chemicals called neurotransmitters into the space of the synapse. These chemicals initiate an electrical impulse in the second nerve cell which then conducts the electrical impulse down the length of its own cell body.
The nerve cell communication is a complex process. The dendrites receive the messages. These chemical messages are then passed down to the cell body and then they reach the axon. Through the axon the messages reaches the connected neuron. You can get details of this process alongwith diagrams at the link below:
They throw the messages in a complex slingshot system