Most died from complication of pneumonia:

"One physician writes that patients with seemingly ordinary influenza would rapidly "develop the most viscous type of pneumonia that has ever been seen" and later when cyanosis appeared in the patients, "it is simply a struggle for air until they suffocate," (Grist, 1979). Another physician recalls that the influenza patients "died struggling to clear their airways of a blood-tinged froth that sometimes gushed from their nose and mouth," (Starr, 1976). The physicians of the time were helpless against this powerful agent of influenza. In 1918 children would skip rope to the rhyme (Crawford):

I had a little bird, Its name was Enza. I opened the window, And in-flu-enza."

A superb paper on the pandemic can be found here.  Other superb resources can be found here.

Of possible interest:

• The 1918-1919 influenza pandemic came in 3 waves over a ~ one year span.  The first wave was not especially fatal like the second wave, but the similarities in the minor and severe cases was unmistakable.
• The virus was identified years later as an H1N1 type of probable avian origin.  Only samples from the second wave were available for DNA sequencing, so it is unclear how this pandemic was different from previous outbreaks/pandemics and how the virus differed in each wave.
• Never before or since the 1918-1919 pandemic has influenza demonstrated such behaviour, not only in its lethality and spread but also in its seeming CHANGE from minor to major infector/killer in the span of a few months.  People infected and survived the 1915 epidemic appeared to be less susceptible to infection and mortality, as were those who were infected during the first wave.  This is a huge question of how something "changed" and became so deadly so quickly.  For a virus to mutate significantly enough to attack a "naive" host and be so deadly (eg a human immune system that has never seen that virus before and has no immunity to it) usually takes years, though minor changes called "antigenic drift" can occur and cause less lethal illness (what the "flu shot" provides protection for oftentimes).  The odds of this occuring again are thought remote without manmade interference.
• Most influenza virii since the 1918-1919 virus/virii ARE related to the 1918-1919 strain(s).  This should confer some immunity for those who have had influenza deriving from that strain in their lives.  The "flu shot" may also confer partial immunity because it contains components that are related to the 1918-1919 strain(s).  Additionally, a couple of the antiviral medications work against the old and new strains, so symptoms may be mitigated in most individuals if treated promptly.
• The overwhelming majority of 1918-1919 influenza deaths were due to pnuemonia, most likely from a secondary BACTERIAL infection.  The virus weakens the immune system and allows bacteria to invade and destroy the lungs.  Mechanical ventilator support and antibiotics will help reduce the severity of illness and number of deaths per unit population as compared to the 1918-1919 pandemic.  Hopefully, advancements in public infectious disease management combined with advances in medicine will reduce deaths and illness.  (The disconnect of the words of the Obama Administration and their actions to the current Swine Flu issue is not encouraging/comforting, IMO)
• Recent research has alledgedly figured out why the 1918-1919 influenza virus was so virulent.  This is good news.  Hopefully this research will guide new diagnostic tests and treatment modalities for future viral infection.
• Even with all the advances in medicine and Public Health, a similarly infective and lethal virus as the one(s) in 1918-1919 combined with an appropriate mixture of seasonal and social conditions would lead to more deaths worldwide because of limitations of medical availability in manpower/equipment/medicines.  Socialized Medicine will do nothing to mediate this situation.  IMO, Socialized Medicine would stifle research and development of medical care modalities.

Now for some related thoughts.  Tamiflu is one of the two antivirals recommended for use in Swine Flu cases.  Interestingly, Tamiflu was deemed to have high rates ineffectivity to H1N1 virus (resistance to the med) by WHO.  Sales of the other antiviral, Relenza spiked since the November 2008 report.  WHO has reported that BOTH Tamiflu and Relenza are effective with the H1N1 Mexican Swine Flu virus, though.  Did Tamiflu luck out or what? 

Will Mexican Swine Flu be good for sales of antivirals?  So far the answer is a qualified yes. 

And just what of the antiviral stockpiles of the US Government?  IIRC, Homeland Security Napolean-tano released 12Million doses of Tamiflu, said to be about 25% of the stockpile.  While this will help pharmaceutical manufacturers bottom line in replacing this, the number of doses will treat about 1.2 Million people only since either treatment or prophylaxis requires 10 pills per person. 

To put this in perspective, 20+ Million (out of 105 Million total population) were sickened in America during the 1918-1919 pandemic.  There are not enough doses of antivirals to go around in the worst case scenario, even considering how quickly that virus killed its host (as little as 1-2 days after a 2 day incubation).  And the whole world will be beg, borrow and stealing available doses.

And if dying from influenza weren't bad enough, All these antiviral medication doses are an "environmental hazard"!  I swear, those Greenies are a buzzkill when the world is trying to get its influenza on.