Exactly when "the Vietnam War" began depends partly on how you define the war. Americans tend to think of it in terms of US troops on the ground, but it makes a lot more sense to go back to 1945, when the Vietnamese declared their independence from Japanese occupation and French colonialism. You could probably trace it back at least to the 1800s, when French seized control of "Indochina," a blanket term for Vietnam, Laos, and Cambodia, and probably even farther back than that. Beginnings in history are generally hard to pin down. But as far as US involvement goes, 1945 is a convenient and not inaccurate starting point.
The French wanted to keep its possessions, and the US, not without some controversy, decided to back imperialism over self-determination. Anti-communism was a handy excuse, since the Viet Minh, the most significant resistance force, was led by Communists. The Vietnamese, who had fought with the Allies against the Japanese, resisted. The fighting escalated, and by 1954 the US was giving France a billion dollars a year in military aid.
I can't really make sense of HowStuffWorks's official answer. It seems to assume that Vietnam was already divided into North and South before 1954, which isn't so. That division was a consequence of the truce line drawn in at the Geneva Conference later that year, and the truce line became a border when the US client dictator in the South, Ngo Dinh Diem, officially refused to hold the referendum required by the truce settlement, and South Vietnam became a separate state.
The North did not attack the South, however, until 1960, when Hanoi finally admitted that the Geneva agreements were a dead letter. Before 1960 the fighting in the South involved Southerners, not all of them Communists, resisting the Diem dictatorship without the support of the North. US aid to Diem's regime increased incrementally throughout that period, including weaponry and US military "advisers," officially just guys from the US government and there to help but in reality getting more and more involved in the fighting. (This was typical of Eisenhower's foreign policy in Southeast Asia; see also the use of American forces in Indonesia, for example.) In 1963 Diem began to lose his will to fight, so the US had him removed and largely took over that side of the fighting, thus commencing "the War in Vietnam" as most Americans think of it today.
So, as I say, HowStuffWorks got the history spectacularly wrong with the first question in its quiz. I don't feel like continuing, or checking out their quiz about the Korean War. But this is a reminder not to be too dismissive of most people's ignorance of history; it takes some work to find accurate accounts, and most people would have no idea how to begin looking for them. Even events in people's own lifetimes are confusing, especially if they happened when one was young. (Last week a student op-ed piece appeared the university newspaper, which exhibited utter confusion over the Birther controversy. My scorn was tempered slightly when I remembered that the writer was still in grade school when Obama was first elected President. It's not an excuse, but it's a partial explanation. I might write more about that piece.) The overall history of US involvement in Vietnam isn't all that murky, but it still involves battered US pride, so it will continue to be distorted. We can expect the same about the War in Terror, but then you knew that, didn't you?
