They were trained at the same bases and in the same manner as those who had enlisted voluntarily. For Army personnel, this usually meant basic training (boot camp) at one of a number of bases, including Fort Ord in California and Fort Hood in Texas. This was followed by Advanced Individual Training (AIT). The location of AIT was dependent on the trade or occupation a man had chosen (if they had volunteered) or been assigned (if they had been drafted). AIT for infantrymen was held at a few different bases, including Fort Polk in Louisiana and Fort McClellan in Alabama. Training for Medics was done at Fort Sam Houston in Texas.

Draftees were deployed to Vietnam in the same manner as volunteers, that is they got orders saying they were going and when. Some men were deployed to South-east Asia straight out of AIT, while others were not. It's important to note that Vietnam was not the only possibility, there was also a chance of being sent to the large standing force the US had in Germany at the time, or remaining stateside. I'm not sure how many draftees ended in Germany as opposed to going to Vietnam, or if it was even possible for a draftee to be sent there.

Once a man arrived in Vietnam, where he went and which unit he was assigned to depended on the needs of the Army. Upon arriving in country, newly arrived soldiers were sent to a replacement depot where they were assigned to their unit. The three main replacement depots were at Cam Ranh Bay, Long Binh, and Da Nang. Draftees ended up serving with virtually every infantry unit deployed to Vietnam, including the 1st, 4th, and 9th Infantry Divisions, the 1st Cavalry Division, and the 101st Airborne Division.

Source: "A life in Year: The American Infantryman in Vietnam" by James R. Ebert, 1993, ISBN: 0-89141-829-6 (Great book if you're interested in learning more about life as an infantryman in the US Army during the Vietnam conflict)