How is a nervous impulse transmitted across a synapse?

An action potential (AP) reaches the pre-synaptic membrane. This causes the voltage-gated calcium channels to open, and calcium ions flow down their concentration gradient into the pre-synaptic terminal. This then causes vesicles containing neurotransmitter (NT) molecules to fuse their membrane with the pre-synaptic membrane. In this way, the NT is released into the synaptic cleft and diffuses across it. When it reaches the post-synaptic membrane, it binds to receptors on its surface, which in turn causes sodium ion channels to open, letting sodium ions to flow down their concentration gradient into the post-synaptic neuron. This generates a new AP in the post-synaptic neuron.