how did submarine warfare bring the U.S. into the world war 1 ?

Answer 1

The Imperial German Navy's U Boat 20 sank the RMS Lusitania on May 7, 1915. The US government sent four diplomatic protests to the German government. The German government replied to the first protest by claiming it regretted the loss of American lives, but the Lusitania had guns on board, and had carried Canadian troops and ammunition on her last voyage.
President Wilson then gave the German government an ultimatum on unrestricted (all boats were "fair game") on April 18, 1916. He brought up the example of the sinking of other passenger ships where the American passengers had lost their lives. For the time, Germany withdrew this policy (unrestricted submarine warfare), but reintroduced the policy in February 1917. The U.S. then broke off diplomatic relations with the German government, the declaration of war soon followed on April 6, 1917.

Answer 2

germans kept sinking passenger ships without warning. and they continued to do it.