The action potential is how neurons are able to propagate electrical messages through itself and release neurotransmitters to communicate with other neurons. The neuron begins at resting potential, which is about -70mV. When it receives a signal, it has to push the membrane potential above –55mV before the rest of the action potential can continue–this is known as “all or nothing,” since the neuron will fire or not fire depending on the change in membrane potential. Once the threshold has been reached, the voltage gated sodium channels open, allowing sodium ions to flow into the neuron and further raise the membrane potential until it gets to its peak, about +35mV. This process is known as depolarization. After that, the sodium ion channels close and the potassium voltage gated ion channels open, allowing potassium ions to flow out of the neuron, which is called repolarization. The potassium channel remains open for a little while longer after the cell reaches resting potential again, and this overshoot is also known as hyperpolarization, after which the potassium channels finally close and the cell reaches its resting membrane potential again with the help of the leakage channels that are always open. This section is also called the refractory period, and the neuron cannot fire during it as the voltage gated sodium channels need time before they can open up again. When the action potential reaches the end of the axon, the vesicles or terminal buttons carrying neurotransmitters release them into the synaptic cleft, the area in between the presynaptic neuron and the postsynaptic neuron.
One way I used to remember where the Na+ and K+ ions are relative to the neuron is by thinking of a banana in the ocean. The banana peel is the cell membrane and has a lot of potassium in it, while the ocean is really salty so the Na+ is outside the cell.