The fact that Americans were taken prisoner is well know but i have never heard of Americans taking prisoners during that war.
Sort of. The Americans decided early on in the war to turn over all prisoners taken, including not only prisoners of war but political prisoners (mostly Viet Cong) as well to the South Vietnamese government. Faced with massive overcrowding, many of these individuals were released within months of capture.
But, so far as the fighting in the field goes, the US military attempted to encourage a strict observance of the Geneva Convention. In November 1965, General Westmoreland met with the South Vietnamese general staff and emphasized the importance of treating prisoners of war properly. In August of the next year, Westmoreland wrote to his major field commanders to say in part, "Active command interest in this program, in coordination with Republic of Vietnam Armed Forces authorities, which assures that prisoners of war and combat captives are properly processed and handled in accordance with International Law is vital." These efforts to enforce the dictates of international law may seem somewhat absurd, given this was a war in which huge amounts of ordnance were dropped or shot in civilian areas, but it was noted by the Red Cross. Samuel A. Gonard, president of that organization, wrote "We are convinced that in the context of the war in Vietnam the U.S. Forces are devoting a major effort to the spread of knowledge of the Geneva Conventions."
http://www.history.army.mil/books/Vietnam/Law-War/law-04.htm
Vietnamese were rounded during operations especially if the were of military age which was seldom. After a cursory screening the were classified as innocent civilian, Vietcong suspect, or Vietcong infrastructure. They were relocated to an Iterrogation of prisoner of compound in a rear area and screened further. Those deemed of intelligence value were then transported to provincial interrogation which was under RVN control with u.s. Personnel at the site.