The Carrington Event

On September first, 1859, Richard Hodgson was observing the Sun, as he usually did, when he noticed a white solar flare.
At the same time, in Redhill, Sussex, Richard Carrigton observed the same phanenoma.  After first seeing it, he believed his equipment to have malfunctioned.  He wrote of the flare,  “I thereupon noted down the time by the chronometer, and seeing the outburst to be very rapidly on the increase, and being somewhat flurried by the surprise, I hastily ran to call someone to witness the exhibition with me.”  A little over 17 hours later, the plasma of the flare would reach the earth.

The Geomagnetic Storm

"Aurora Borealis." 1865 Frederic Edwin Church 

The plasma from those flares hit the earth between September 2nd and 3rd, causing auroras around the world; yet it followed days of sunspot activity.  On August 29, Queensland, Australia reported Auroras.  Those in September stretched beyond the far north, reaching as far south as the Caribbean and Colombia, filling the sky with greens, reds, and purples.  They were bright enough in the Northeastern United States that one could read a newspaper by their light.  Goldminers in the Rocky Mountains awoke and prepared breakfast, as they thought it was morning by the light.  It was between 8 and 10 o'clock at night.

An Australian gold miner, by the name of C. F. Herbert, wrote in a letter to the editor after seeing that the Arouras, that "[he] thought it a foreshadowing of Armageddon and final dissolution."

Telegraphs

In the late 1850s, only Europe and the Eastern United States had operational telegraph systems of scale, while India and Australia had a few lines, and Japan was still in the experimental development.  In Europe, they stretched from Königsburg, Prussia, to Cork, Ireland, criss-crossing what is now Germany, northern Italy, France, and Great Britain.  But Spain, southern Italy, and the Ottoman Empire were devoid of telegraph lines, and the lines in the Austro-Hungarian empire were much longer than their Western European counterparts, which were more susceptible to ground induced currents, which would become problematic in this September.  

Telegraphs began to fail near midnight on August 29th, when Brussels lost contact with other European Capitals.  Operators noticed the auroras over Brussels and Paris at the time.  Around 3 am, they tried to regain contact with London by using batteries to control the cables, overpowering the induced currents.  They were successful, and did not damage the cables.

The same cannot be said of most of the Americans' attempts.  When the stations tried to combine the induced current with the direct currents of the batteries, sparks would fly.  Combined with organisational skills that improperly stowed paper and chemicals, many telegraph stations caught fire.    The sparks also stunned at least one operator, Fredrick Royce, who recounted his story as follows.  

"During the display I was calling Richmond, and had one hand on the iron plate. Happening to lean towards the sounder, which is against the wall, my forehead grazed a ground-wire which runs down the wall near the sounder. Immediately, I received a very severe electric shock, which stunned me for an instant. An old man who was sitting facing me, and but a few feet distant, said that he saw a spark of fire jump from my forehead to the sounder. The Morse line experienced the same difficulty in working." [New York Times, September 5, 1859.]

Now some stations that managed to evade such catastrophes, as a documented exchange between Portland and Boston shows.

Boston - "[Our batteries are] also disconnected, and we are working with auroral current.  How do you receive my writing?" 

Portland - "Better than with our batteries on.  Current comes and goes gradually."

See more of the exchange here.

The reports from India show no interference to telegraph lines.  It is theorised that the sedimentary characteristics of the soil near Mumbai contributed to it. 

After the Storm

Economic effects were marginal.  There were some newspapers that relied on telegraph communications, but they did not lack information during or after the storm.  The telegraph stations were able, after a few hours, to return to normal functioning, without creating an enormous backlog of messages.
Ozone amounts in the troposphere increased by around 20% between the 28th and the 29th (notably on the earlier side of the activity), due to the increase of UV radiation that reached the troposphere.  This could be dangerous, but mortality records in 1859 and 1860 do not show any abnormalities.

If it Happened Today

These geomagnetic storms impact electrical circuits, so everything with one would be impacted and damaged.  Most estimates put the damages at 1-2 trillion US dollars, though some have set it as high as 20.  

It would impact and destroy satellites, bank accounts, the stock exchange, the power grid, and kill any astronauts on spacewalks.  Without satellites, any GPS would be unable to function, planes would be grounded, and cell phone reception would be a thing of the past.

If radar picked up the solar flare, as it did for a smaller one in 1967, it could be read as a nuclear missile launch, and lead to a nuclear war.

On a more positive note, it is thought that these storms appear only every five hundred years, although the data is too scarce for a definite answer.

Personal accounts of the Auroras:

https://www.thesocialhistorian.com/carrington-solar-flare-of-1859/
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050210157.pdf

Further Analysis of the Storm and its impacts:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4669545/