What type of fighting did the germans use? what did it do to the lusitania?

Germans used U-boats (abbreviated from unterseeboot, which means undersea boats) to destroy ships that traded between the US and Great Britain. One german U-boat torpedoed the Lusitania and it sunk on May 7 ,1915.

I assume you mean naval fighting, as you mentioned the Lusitania. Prior to the First World War, the German Navy (the Kriegsmarine) had built up a small force of Unterseebooten, or U-boats, a type of quick and stealthy torpedo armed submarine.
  Although the German Kriegsmarine possessed only 38 of the craft at the outset of the conflict, they incurred massive losses against British and French shipping, striking a heavy blow to Great Britain's and France's ability to import food for their armies and citizens as well as equipment for their armies. Much of what Britain and France were shipping came directly from the United States, thus the German attacks on these trade convoys strained US - German relations considerably. 
  In 1915, German U-Boat U-20 patrolling of the coast of Ireland spotted a British cargo and passenger liner known as the RMS Lusitania. The captain of U-Boat U-20 believed that the Lusitania was carrying supplies and munitions to be delivered to the British government, however the Lusitania was actually carrying a large number of American civilians. The U-Boat sunk the Lusitania, killing every American on board.
  This senseless loss of American life at the hands of the German Kriegsmarine prompted quite a lot of rage amongst the American populace, and would later be cited as one of America's motivations to enter the war in 1917.