How did World War I help to bring about the Russian Revolution?
Russia entered WWI as a result of Czar Nicholas II's appallingly bad judgement.
The kings of (among other countries) England, Germany and Russia were all first cousins--they were grandsons of Victoria--but royals are different from you and me. Czar Nicholas II saw World War I as an opportunity to improve the Russian economy, and in general saw war as the only way to do so. Russia's defeat in the Russo-Japanese War of a few years earlier would have dissuaded most other monarchs from trying such a strategy again, but Nicholas was undeterred.
Sending the army to fight in World War I gave the Bolsheviks an opportunity to wage their revolution virtually unopposed. They had tried to mount popular revolution once or twice before, but the Czar's army was around to keep them in check--until it suddenly wasn't.