You can see the actual photograph on the photographers homepage.  There were at least 3 upward discharges initiated by the approach of the stepped leader (1, 2, and 3 in the sketch).  Streamer 1 connected to the bottom of the stepped leader.  It isn't clear where the exact junction point was.  The downward branching at Point 4 indicates that was part of the descending stepped leader.  A very faint upward discharge can be seen at Point 3.  Here's another more recent photograph (click on Galleries on the bar near the top of the page, then click on Lightning Gallery 1). 

Lightning rods (invented by Benjamin Franklin) make use of the upward connecting discharge.

A powerful current travels back up the channel from the ground toward the cloud.  This is the 1st return stroke.  Large currents (typically 30,000 amps in this 1st return stroke) heat the air to around 30,000K (5 times hotter than the surface of the sun) which causes the air to explode.  When you hear thunder, you are hearing the sound produced by this explosion.

The figure below shows what we've covered so far in simplified form

A downward negatively charged stepped leader followed by a positively charged upward moving return stroke.

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Many cloud-to-ground flashes end at this point.  In about 50% of cloud to ground discharges, the stepped leader-upward discharge-return stroke sequence repeats itself (multiple times) with a few subtle differences.

The sketch above and the photo below show a multiple stroke flash consisting of 4 separate return strokes. There is enough time between separate return strokes (around 1/20th to 1/10th of a second) that your eye can separate the individual flashes of light.

Here are some unusual types of lightning.

We've been looking at strikes that originate in the negative charge center is a thunderstorm (discharge at left in figure above).  Occasionally a lightning stroke will travel from the positive charge region in the top of the thunderstorm cloud to ground (shown at right in the figure above).  These types of strikes are more common at the ends of storms and in winter storms.  This is probably because the top part of the cloud gets pushed sideways away from the middle and bottom portions of the cloud.  Positive strokes are very powerful.  They sometimes produce an unusually loud and long lasting clap of thunder.

Here's an even rarer form of lightning.  Lightning sometimes starts at the ground and travels upward.  Upward lightning is generally only initiated by mountains and tall objects such as a skyscraper or a tower of some kind (the Empire State Building is struck many times every year but lightning and usually it's lightning that the building itself caused). 

Note the discharge is different in another way also.  These discharges are initiated by an upward leader.  This is not followed by a return stroke, like you might expect, but by a more normal downward leader.  Once the 2nd leader reaches the ground, an upward return stroke travels back up the channel to the cloud.

The fact that lightning could begin with an upward discharge that begins at the ground led (French) scientists to develop a technique to trigger lightning by firing a small rocket up toward a thunderstorm.  The rocket is connected by a thin wire to the ground.  When the rocket gets 50 to 100 m above the ground an upward streamer will develop off of the top of the wire.  Once the streamer reaches the cloud it can initiate a "normal" series of downward dart leaders and upward subsequent return strokes.

When lightning strikes the ground it will often melt the soil (especially sandy soil) and leave behind a rootlike structure called a fulgurite.  A fulgurite is just a narrow (1/2 to 1 inch across) segment of melted sand (glass). 

Stay away from tall isolated objects during a lightning storm.  You can be hurt or killed just by being close to a lightning strike even if you're not struck directly.  Lightning currents often travel outward along the surface of the ground (or in water) rather than going straight down into the ground.  Just being close to something struck by lightning puts you at risk.

An automobile with a metal roof and body provides good protection from lightning.  Many people think this is because the tires insulate the car from the ground.  But the real reason cars are safe is that the lightning current will travel through the metal and around the passengers inside.  The rubber tires really don't play any role at all.  The people in Florida in the video that were triggering lightning with rockets were inside a metal trailer and were perfectly safe.  All of the connections made to equipment outside the trailer were done using fiber optics, there were no metal wires entering or leaving the trailer.