The Vietnam War actually started in Vietnam with the end of World War II. Real trouble began when France, after 100 years of controlling the territory was forced out. This timeline should tell you something about the political happenings and a few of the major battles.
1962
December: First U.S troops are deployed to South Vietnam.
1963
June: In protest of the Diem Government, the first of many Buddhist Monks sets himself on fire.
November: Ngo Dinh Diem, the president of South Vietnam is murdered by his South Vietnamese generals. There are now approximately 16,500 U.S. troops in South Vietnam.
1964
February: 5,000 more U.S. troops are sent to South Vietnam as hostility in the region is rising.
July: 500 Vietcong soldiers cross the South Vietnam border and seize three strategic hamlets.
1965
January: More then half there soldiers are lost as South Vietnam suffers a defeat at Binh Gia.
March: President Lyndon B. Johnson sends more U.S Marines and also send the first U.S. combat troops.
May: Trying to help promote peace talks the U.S briefly stops air raids, and then peace talks fall out and bombing continues.
December: Bombing again halts again trying to promote peace talks.
1966
March: One of the biggest U.S base in the region is wiped out along with with more then half the people stationed there.
September: The U.S. launches the biggest bombing campaign of the war, more then 500 B-52's are used.
1967
April-May: In one of the longest and bloodiest battles of the whole war, the United States defeats the North Vietnamese and the Vietcong. 160 U.S. men were killed, and 764 wounded. While the North Vietnamese suffered 940 casualties.
At the end of 1967 the United States had over half -a-million people in Vietnam. 9,353 United States soldiers are killed in 1967 alone.
1968
March: The United States and the world are stunned when then President Lyndon B. Johnson announces that he will not run for reelection for president.
1969
December: New American President Richard Nixon begins to withdraw troops from Vietnam.