The hair on end is created when the channel/path for the return strike is created.
Close, but not quite right. Lightning is caused by an electric charge which builds up in rain clouds under the correct conditions. One necessary condition is the formation of hail within the cloud, near the top where it is held by powerful updrafts. Water condenses on the hail particles, freezes causing the hail to get heavier and fall. As the hail drops it encounters warmer air which melts some ice from the particle. When enough is melted the updraft mill cause the lightened ice to return to the cloud top.
This lifting and dropping acts to separate static electricity (generated by the turbulent up & down drafts) into positive and negative areas at the top and bottom of the thunder head cloud. Electric charges of the same polarity repel each other, thus the bottom of the cloud is evenly covered with charged particles of the same polarity.
As the surface winds move the clouds sideways relative to the earth, the charged bottom (which may be several acres in extent) is mirrored by a similarly sized sheet of opposite polarity traveling along the ground. This happens because unlike charges attract. The charged bottom of the cloud and the charged mirroring it on the ground move along together because of the electrostatic attraction. The distance between these two charged areas (air gap) serves to keep the charges separated. As the cloud moves along the charges keep trying to annihilate the potential difference between cloud and ground.
As the cloud moves you might notice short leaders jumping from the ground upwards toward the cloud above (St. Elmo's Fire). The leaders are trying to make a connection and will form on anything that reduces the air gap. If they are visible it's time to lay as flat as possible.
If you are near a tall tree or metal tower they will always attract lightning and should be avoided because of secondary effects.
A strike is initiated when a leader from the ground reaches upward and joins a leader from the cloud reaching down. The areas of charge on the cloud bottom and on the ground are both spread over a large area. When the leaders make contact, they establish a very narrow path by ionizing the air in the gap which may be a foot or so in diameter. Once the arc is started all of the charged particles on the cloud bottom (several acres in extent) rush to join in the current flow through ionized leader path to ground. Currents in the million amp range may flow and heat up the air which causes it to violently expand and produce thunder.
Often missed by people discussing lighting are secondary effects. Once the strike is passing a very large current (a million amps) which is flowing sideways from the edges of the charged area to the ionized connection. This is also a current, mirrored by the charges flowing through the ground. Now you have a million amps flowing sideways through the ground This will generate an extremely strong electromagnetic pulse. Any metal objects (telephone wires, stove pipes, copper pipes, electric fence wires &c, &c fiber optic cables no problem) will act as an air core transformer and induce a charge of several tens of thousands Volts as the charge eventually dissipates. (My brother had a private well with a submersible pump. The pump stopped working after a thunder storm passed through the area, the motor was burned out even though it was 85' below ground and under water!)
The actual voltages are not DC nor AC as such because there are inductive and capacitive elements which produce a damped oscillation.
PS trees are very bad Ju-Ju as a lightning strike will pass through the bark and burn a conductive path through the sap, which boils to steam and is known to cause a nasty explosion.
Regards,
GtG
PS Hope that clears everything up...