Here is a summary of the sequence of events that take place in synaptic transmission from a presynaptic neuron to a postsynaptic cell.  Each step is explained in more detail below.  Note that with the exception of the final step, the entire process may run only a few hundred microseconds, in the fastest synapses.
#The process begins with a wave of electrochemical excitation called an action potential traveling along the membrane of the presynaptic cell, until it reaches the synapse.
#The electrical depolarization of the membrane at the synapse causes channels to open that are permeable to calcium ions.
#Calcium ions flow through the presynaptic membrane, rapidly increasing the calcium concentration in the interior.
#The high calcium concentration activates a set of calcium-sensitive proteins attached to vesicles that contain a neurotransmitter chemical.
#These proteins change shape, causing the membranes of some "docked" vesicles to fuse with the membrane of the presynaptic cell, thereby opening the vesicles and dumping their neurotransmitter contents into the synaptic cleft, the narrow space between the membranes of the pre- and postsynaptic cells.
#The neurotransmitter diffuses within the cleft.  Some of it escapes, but some of it binds to chemical receptor molecules located on the membrane of the postsynaptic cell.
#The binding of neurotransmitter causes the receptor molecule to be activated in some way.  Several types of activation are possible, as described in more detail below.  In any case, this is the key step by which the synaptic process affects the behavior of the postsynaptic cell.
#Due to thermal vibration, the motion of atoms, vibrating about their equilibrium positions in a crystalline solid, neurotransmitter molecules eventually break loose from the receptors and drift away.
#The neurotransmitter is either reabsorbed by the presynaptic cell, and then repackaged for future release, or else it is broken down metabolically.