The American campaign begins with Private Joe Martin, member of the 506th Parachute Regiment, training at Camp Toccoa, in Georgia, United States on 9 August 1942. This is meant to familiarize the player with the game controls. The first mission occurs toward midnight on June 5, 1944, as part of the airborne missions which began the invasion of Normandy.

The British campaign. The first mission of the British campaign has Sergeant Jack Evans and a unit from the 2nd Ox and Bucks of the 6th Airborne Division take part in Operation Tonga. The third mission, on 2 September, has Evans working alone, now with the Special Air Service or SAS. He is inserted next to the Eder Dam and destroys the anti- aircraft guns protecting it. During Operation Chastise the previous May, a squadron destroying the dam using bouncing bombs. The seventh and final mission of the British campaign shows Evans, Waters and their squad near Burgsteinfurt, Germany with their objective to destroy mobile V2 rockets and key German supplies. Evans, Waters and their squad successfully destroy the V2 rockets.

The first Soviet mission occurs during the Battle of Stallingad, on 18 September 1942. Corporal Alexei Ivanovich Voronin is on one of many barges transporting Soviet soldiers across the Volga River, many of which are destroyed on the way by German artillery or Luftwaffe aircraft. Once across, Voronin is unarmed and must avoid machine gun fire and find an experienced sniper to help him. Soviet artillery eventually clears out the German machine guns, allowing Voronin and the others to enter Red Square. In the final mission, on 30 April 1945, Sergeant Voronin is returned to the 150th Rifle Division. His unit battles of Berlin to reach the Reichstag building, and they raise the Victory Banner atop the building.

http://en.wikipedia.org/wiki/Call_of_Duty_(video_game)#Gameplay