In a non-myelinated neuron, an action potential is triggered when a stimulus opens voltage-gated sodium channels, causing sodium ions to diffuse into the neuron and depolarize the membrane. This depolarization then triggers adjacent areas of the neuron to open their sodium channels, creating a domino effect that propagates the action potential along the axon. After transmission, potassium channels open, allowing potassium ions to flow out and repolarize the membrane, restoring the resting potential between activations.